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Date  Due 


JAN  14  1994 


FEB27  1993 


HOME  UNIVERSITY  LIBRARY 
OF  MODERN  KNOWLEDGE 

No.  43 

Editor •J.- 
HERBERT   FISHER,  M.A.,  F.B.A. 
PROF.  GILBERT  MURRAY,  LiTT.D., 

LL.D.,  F.B.A. 

PROP.  J.   ARTHUR    THOMSON,  M.A. 
PROF.  WILLIAM  T.  BREWSTER,  M.A. 


A  complete  classified  list  of  the  volumes  of 
HOME     UNIVERSITY    LIBRARY    already    published 
will  be  found  at  the  back  of  this  book. 


MATTER 
AND    ENERGY 

BY 
FREDERICK   SODDY 

M.A.,    F.R.S. 

LECTURER  IN  PHYSICAL  CHEMISTRY  AND  RADIOACTIVITY 
UNIVERSITY  OF  GLASGOW 


NEW  YORK 
HENRY  HOLT  AND   COMPANY 

LONDON 
WILLIAMS   AND   NORGATE 


COPYRIGHT,  1911, 

BY 

HENRY    HOLT  AND    COMPANY 


THE  UNIVERSITY   PRESS,    CAMBRIDGE,    U.S.A. 


CONTENTS 


CHAP.  PAGE 

PERIODIC  TABLE  OF  THE  ELEMENTS 6-7 

I   PHYSICAL  HISTOKY 9 

II   MATTER  :   I.  ATOMS  AND  MOLECULES     ....  38 

III  MATTER  :   II.  THE  ELEMENTS 58 

IV  HEAT  AND  THE  KINETIC  THEORY  OF  MATTER    .  71 
V   POTENTIAL  AND  CHEMICAL  ENERGY 105 

VI   ELECTRONS  AND  X-RAY8 144 

VII  INERTIA 164 

VIII   RADIATION 183 

IX   RADIOACTIVITY 197 

X  COSMICAL  ENERGY 232 

BIBLIOGRAPHY 254 

INDEX  .                                                                    .  255 


2075630 


PERIODIC  TABLE 


GROUP  0. 

GROUP  L 

GROUP  IL 

GROUP  IIL 

GROUP  IV. 

GROUP  V. 

Helium 
He  8-99 

Lithium 
Li  6-94 

Beryllium 
Be  9-1 

Boron 
Bll-0 

Carbon 
C  12-00 

Nitrogen 
N  14-01 

Neon 
Ne  20-2 

Sodium 
Na  23-00 

Magnesium 
Mg  24-32 

Aluminium 
AI27-1 

Silicon 
Si  28-3 

Phosphorus 
P  31-04 

Argon 
A  39  -88 

Potassium 
K  39-10 

Calcium 
Ca  40-07 

Scandium 
SC44-1 

Titanium 
Ti  48-1 

/Vanadium 
\     V  51-0 

Copper 
Cu  63-57 

Zinc 
Zn  65-37 

Gallium 
G&69-9 

Germanium  \ 
G«  72-5     / 

Arsenic 
As  74-96 

Krypton 
Kr  82-92 

Rubidium' 
Rb  58-45 

Strontium 
Sr87-63 

Yttrium 
Yt89'0 

Zirconium 
Zr90'6 

/Niobium 
\  Nb  93-5 

Silver 
Ag  107-88 

Cadmium 
Cd  112-40 

Indium 
In  114-8 

Tin       \ 
Sn  119-0  ) 

Antimony 
Sb  120-2 

Xenon 
Xe  130-2 

Caesium 
Ca  132-81 

Barium 
Ba  137-37 

[Lanthanum                Cerium 
La  139-0                  Ce  140'26 

Europium                   Gadolinium                   Terbiun 
Eu  162-0                         Gd  157-3                         Tb  169' 

Thulium              Ytterbium             LuteciumT 
Tm  168-8                 Yl)  172-0                 Lul74-oJ 

i 
2 

/  Tantalum 
\   Tal81-5 

Gold 
Au  197-2 

Mercury 
Hg  200-6 

Thallium 
Tl  204-0 

Lead     \ 

Pb  207-10  / 

Bismuth 
Bi  208-0 

Radium 
Emanation 
222- 

Radium 
Ra  226-4 

Thorium 
Th  232-4 

OF  THE  ELEMENTS 


GROUP  VL 

GROUP  VII. 

GEOOT  VIIL 

«B5 

Fluorine 
F19-0 

Sulphur 
S  82-07 

Chlorine 
Cl  35-46 

Chromium 
Cr  52-0 

Manganese 
MA  54  93 

Iron                    Cobalt                   Nickel 
Fe  55-84                 Co  68-97                  Ni  W68 

Selenium 
8e79-2 

Bromine 
Br  79-92 

Molybdenum 
Mo  96-0 



Ruthenium          Rhodium         Palladium 
Ru  101-7             Rn  1W-9            Pd  106'7 

Tellurium 
Te  127-5 

Iodine 
1  126-92 

Praesodvmium          Neodymium          Samariuta 
Pr  140-6                   Nd  144-3               Sa  150'4 

Dysprosium                 Erbium 
Dy  162-6                   Er  1677 

Tungsten 
W  184-0 



Osmium              Iridium              Platinum 
08190-9               Ir  193-1                Pt  195-2 

(Polonium) 

Uranium 
U  238-5 

MATTER  AND  ENERGY 


CHAPTER  I 

PHYSICAL  HISTORY 

THE  behaviour  of  matter  and  energy 
represents  one  aspect  only  of  human  knowl- 
edge, which  is  generally  known  by  the  name 
of  physical  science.  It  seems  well  to  state 
at  the  outset  that,  throughout  these  pages, 
when  the  term  science  is  employed  it  refers 
solely  to  this  one  branch.  Physical  science 
enjoys  the  distinction  of  being  the  most 
fundamental  of  the  experimental  sciences, 
and  its  laws  are  obeyed  universally,  so  far 
as  is  known,  not  merely  by  inanimate  things, 
but  also  by  living  organisms,  in  their  minutest 
parts,  as  single  individuals,  and  also  as  whole 
communities.  It  results  from  this  that, 
however  complicated  a  series  of  phenomena 
may  be  and  however  many  other  sciences 
may  enter  into  its  complete  presentation, 

9 


10  MATTER  AND  ENERGY 

the  purely  physical  aspect,  or  the  application 
of  the  known  laws  of  matter  and  energy, 
can  always  be  legitimately  separated  from  the 
other  aspects.  This  aspect  comes  first,  not 
necessarily  in  relative  importance,  but  in  the 
order  of  the  scientific  definition  of  the  phe- 
nomena and  of  the  problems  it  presents  for 
a  solution.  A  great  simplification  thereby 
results,  which  is  too  often  neglected.  Com- 
plete ignorance  of  these  laws  is,  nowadays, 
rare,  for  they  enter  into  the  general  common 
sense  of  the  age,  and  any  flagrant  violation 
of  them  is  quickly  exposed.  But  the  neglect 
to  give  precedence  to  the  purely  physical 
aspect  of  the  complicated  occurrences  and 
events  of  human  experience  in  their  orderly 
presentation,  has  led  to  much  confused 
history  and  a  general  lack  of  clearness  as  to 
the  precise  terms  with  Nature  on  which  the 
race  exists  on  this  planet.  There  is  a  special 
branch  of  study  known  as  physical  geography, 
but  the  need  for  a  similar  branch  of  physical 
history  does  not  appear  to  have  been  widely 
felt.  The  laws  expressing  the  relations 
between  energy  and  matter  are,  however, 
not  solely  of  importance  in  pure  science. 
They  necessarily  come  first  in  order,  in  the 
fundamental  sense  described,  in  the  whole 
record  of  human  experience,  and  they  control, 


PHYSICAL  HISTORY  11 

in  the  last  resort,  the  rise  or  fall  of  political 
systems,  the  freedom  or  bondage  of  nations, 
the  movements  of  commerce  and  industry, 
the  origin  of  wealth  and  poverty,  and  the 
general  physical  welfare  of  the  race.  If  this 
has  been  too  imperfectly  recognized  in  the 
past,  there  is  no  excuse,  now  that  these 
physical  laws  have  become  incorporated  into 
everyday  habits  of  thought,  for  neglecting 
to  consider  them  first  in  questions  relating 
to  the  future.  It  is  an  interesting  and  by 
no  means  hackneyed  side  of  the  subject  to 
consider,  so  far  as  the  operation  of  purely 
physical  laws  can  teach,  exactly  what  the 
future  has  in  store  for  this  world  and  the 
complicated  civilisation  that  it  contains.  Is 
it  a  stable  and  permanent  movement,  or  does 
it  carry  in  itself,  like  the  life  of  the  individuals 
that  comprise  it,  the  seeds  of  its  own  inevi- 
table decay?  Moreover,  if,  as  will  transpire 
when  the  nature  of  the  controlling  physical 
laws  has  been  made  clear,  it  is  ephemeral  and 
will  decline  the  sooner  the  more  rapid  its 
development  and  the  more  glorious  the  zenith 
it  attains,  what  alteration  of  the  existing  con- 
ditions would  suffice  to  convert  it  into  a 
physically  stable  and  permanent  movement? 
On  these  great  questions,  rendered  the  more 
fascinating  because  of  the  disposition,  since 


12  MATTER  AND  ENERGY 

the  development  of  the  doctrine  of  evolution, 
to  consider  the  fate  and  future  of  the  indi- 
vidual as  of  little  importance  compared  with 
the  fate  and  future  of  the  species,  physical 
science  in  its  later  developments  has  much  to 
say  that  is  of  general  interest.  The  proverb 
counselling  the  cobbler  to  stick  to  his  last  is  a 
good  one;  but  since  the  province  of  physical 
science  is  the  universe  and  all  that  moves 
therein,  its  right  to  be  heard  first,  in  order  of 
presentation  of  the  subject  only,  cannot  be 
withstood.  It  may  or  may  not  assist  in  dis- 
closing the  fundamental  bearings  of  any 
question,  but  anything  it  has  to  say  will  in 
general  be  definite  and,  in  so  far  as  the  laws 
are  perfectly  known,  incapable  of  being  inval- 
idated by  any  other  considerations  whatever. 
The  laws  may  not  be  fully  known  and  may 
give  rise  to  false  deductions,  a  case  of  which 
arose  in  the  question  of  the  duration  of  geo- 
logical time.  In  such  a  case,  the  discussion  of 
the  conflicting  evidence  can  only  result  in  the 
advance  of  knowledge.  Physical  science,  by 
reason  of  the  universality  of  its  laws,  has 
something  to  say  on  almost  every  subject. 
It  need  only  be  stated  once  for  all,  that 
although  the  purely  physical  side  can  be 
considered  separately,  it  does  not  render 
other  points  of  view  less  necessary,  though,  of 


PHYSICAL  HISTORY  15 

course,  it  is  only  with  the  physical  point  of 
view  that  the  present  volume  is  concerned. 
To  adopt  for  the  moment  the  language  of 
Spencer's  Classification  of  the  Sciences,  referred 
to  in  the  Introductory  volume  of  this  Series 
(p.  89),  physical  science  supplies  subject- 
matter  for  every  actual  occurrence  in  the 
universe,  but  none  of  the  truths  outside  of 
physical  science  can  help  in  the  solution  of 
physical  problems. 

The  recognition  of  the  fundamental  physi- 
cal conditions  which  control  the  destinies  of  a 
race,  too  often  occurs  too  late  in  its  develop- 
ment to  be  of  service.  History  throws  some 
strange  sidelights  on  this  blindness  to  the 
obvious.  The  upward  progress  of  the  race 
has,  for  example,  been  classified  into  succeed- 
ing eras,  each  designated  by  the  name  of  a 
material.  Thus  are  distinguished  the  Stone 
Age,  the  Bronze  Age,  the  Iron  Age,  and  the 
Steel  Age.  The  names  indicate  that  the  era 
in  question  was  associated  with  a  certain 
degree  of  mastery  over  a  particular  material 
sufficient  to  enable  new  weapons  to  be  forged 
in  the  struggle  for  existence.  Yet,  when  the 
early  records  of  these  eras  are  examined, 
little  or  nothing  is  found  about  the  pioneers 
whose  knowledge  and  craft  effected  these 
broad  advances.  Often  were  Ijhey  held  in 


14  MATTER  AND  ENERGY 

such  contempt  that  it  was  considered  almost 
beneath  the  dignity  of  an  educated  man  even 
to  make  himself  superficially  acquainted  with 
the  technical  processes  to  which,  in  the  judg- 
ment of  history,  his  era  owed  its  initiation. 
To  come  to  more  recent  times,  how  many 
people  blessed  with  a  liberal  education  would 
be  at  a  loss  if  asked  offhand  what  steel  is, 
and  how  it  is  distinguished  from  iron;  or 
would  recognise  even  the  names  of  the  great 
founders  of  the  modern  era? 

Fundamental  as  materials  are  in  shaping 
the  broad  lines  of  progress,  it  is  necessary  to 
go  but  very  little  deeper  to  come  upon 
something  equally  fundamental  but  less  ob- 
viously so.  Materials  are  employed  merely 
as  weapons,  tools,  or  instruments  for  the 
utilisation  of  power  or  energy.  Even  the 
food  we  eat  is  not  the  end  but  the  means  of 
living.  Life  is  physically  distinguished  from 
death  by  movement,  and  what  food  is  to 
the  motion  of  living  organisms,  fuel  is  to 
the  motion  of  mechanical  engines.  With 
the  advent  of  steel  the  utilisation  of  the 
natural  sources  of  energy  has  progressed 
with  enormous  strides.  Less  than  a  hundred 
years  ago  little  was  known  about  energy, 
and,  indeed,  the  modern  idea  of  energy  as 
a  definite  fundamental  existence  was  not 


PHYSICAL  HISTORY  15 

developed  till  well  on  in  the  last  century. 
Isolated  examples  of  energy,  apart  from  that 
of  living  beings,  have  been  known  necessarily 
and  some  have  been  utilised  from  the  re- 
motest times.  The  wind  that  propels  the 
sailing  ship  was  probably  one  of  the  first 
forms  to  be  harnessed  to  the  affairs  of  life. 
The  phenomena  of  fire,  and  the  thermal 
energy  derived  from  it,  were  known  to  all 
but  the  most  primitive  races,  though  its 
recognition  as  one  of  the  manifestations  of 
energy  is  not  yet  a  century  old.  Not  until 
the  law  of  the  conservation  of  energy  was 
established,  and  it  was  shown  that  energy  like 
matter  is  indestructible  and  uncreatable, 
could  energy  be  regarded  as  one  of  the 
fundamental  physical  existences.  Its  recog- 
nition, as  a  separate  entity,  distinguishes 
the  present  age  from  all  its  predecessors. 
This  is  the  Age  of  Energy,  or  rather  this  is 
the  beginning  of  the  ages  of  energy,  the 
Age  of  the  Energy  of  Coal.  The  triumphs  of 
this  age  have  been  sung  in  season  and  out  of 
season.  Already,  however,  science  has  out- 
grown such  immature  jubilation.  That  this 
still  is  the  age  of  the  energy  of  coal  is  un- 
fortunately only  too  true,  and  the  whole 
earth  is  rendered  the  filthier  thereby.  More- 
over, the  age  will  last  just  so  long  as  the 


16  MATTER  AND  ENERGY 

coal  supply  lasts,  and  after  that  the  last 
state  of  the  race  will  be  worse  than  the  first, 
unless  it  has  learned  better.  Only  ten  years 
ago  the  prospect  was,  in  fact,  anything  but 
a  cause  for  jubilation;  but  these  last  years 
have  wrought  a  wonderful  revolution  in  our 
knowledge  of  energy,  and  therefore  in  the 
future  outlook  of  the  race,  now  entirely 
bound  up  with  that  of  energy.  It  is  possible 
to  look  forward  to  a  time,  which  may  await 
the  world,  when  this  grimy  age  of  fuel  will 
seem  as  truly  a  beginning  of  the  mastery  of 
energy  as  the  rude  stone  age  of  paleolithic 
man  now  appears  as  the  beginning  of  the 
mastery  of  matter.  It  may  await  the  world, 
but  by  no  means  of  necessity  awaits  it. 
The  prospect  is  physically  possible,  but  the 
realisation  depends  also  upon  man  and 
whether  he  can  ever  hope  to  rise  to  the 
heights  of  knowledge  the  problem  demands. 
The  discoveries  in  connection  with  the 
recently  explored  field  of  radioactivity  have 
put  an  entirely  different  complexion  on  the 
question  as  to  how  long  the  energy  resources 
of  the  world  may  be  expected  to  last.  It 
has  transpired  that  there  exists  in  matter, 
associated  with  its  ultimate  atoms,  that  is, 
by  definition,  with  the  smallest  particles 
capable  of  separate  existence  of  the  elements 


PHYSICAL  HISTORY  17 

or  most  fundamental  known  forms  of  matter, 
sufficient  potential  energy  to  supply  the 
uttermost  ambitions  of  the  race  for  cosmical 
epochs  of  time.  But,  just  in  proportion  as 
the  prizes  to  be  won  by  the  progressive 
mastery  over  the  physical  universe  become 
the  more  magnificent,  the  more  does  their 
achievement  transcend  in  difficulty  and 
seeming  impossibility  the  older  successes. 
Think  of  the  ages  that  elapsed  after  man 
kindled  his  first  fire,  before  the  world  hummed 
to  the  tune  of  the  steam  engine.  Think  of 
the  ages  that  preceded  even  this  remote 
discovery,  so  ancient  that  no  record  of  it 
survives,  during  which  in  natural  conflagra- 
tions man  must  have  been  made  aware  of 
the  energy  in  fuel  before  he  had  learned  how 
to  liberate  it  at  will.  With  reference  to 
the  newly  revealed  stores  of  atomic  energy  in 
matter,  and  to  the  time,  so  lightly  pictured  in 
the  imagination,  when  it  may  raise  the  race  to 
the  loftiest  pinnacle  of  its  ambitions,  we  are 
in  the  position  that  savage  man  bears  to  the 
present,  aware,  but  in  every  other  way 
ignorant.  True  we  are  thoroughly  familiar 
with  the  more  superficial  processes  of  nature, 
and  bring  to  the  task  a  trained  and  disciplined 
intelligence.  But  the  task  increases  in  pro- 
portion to  the  knowledge  which  defines  it. 


18  MATTER  AND  ENERGY 

Practically  King  Coal  is  as  likely  as  ever  to 
die  naturally  of  exhaustion  as  to  be  deposed 
by  another  monarch;  and,  if  so,  he  carries 
away  with  him  the  means  of  subsistence  of 
our  boasted  civilisation.  But  the  recognition 
of  the  boundless  and  inexhaustible  energy  of 
Nature,  and  the  intellectual  pleasure  and 
gratification  it  affords,  brightens  the  whole 
outlook  of  the  twentieth  century. 

Mere  accumulations  of  knowledge,  sifted, 
classified,  and  reduced  to  their  final  most  con- 
cise expression  in  a  series  of  text-books,  are 
little  more  than  the  sepulchral  monument  of 
science.  However  complete  and  accurate, 
mere  knowledge  deadens  rather  than  develops 
the  intellect.  The  history  of  the  winning  of 
knowledge  preserves  a  sparkle  of  life  and  may 
stimulate  as  well  as  instruct.  But  the  real 
value  of  science  is  in  the  getting,  and  those 
who  have  tasted  the  pleasure  of  discovery 
alone  know  what  science  is.  A  problem 
solved  is  dead.  A  world  without  problems 
to  be  solved  would  be  devoid  of  science 
though  it  might  be  full  of  scientific  text- 
books and  dictionaries.  Such  is  the  prospect 
that  recent  discoveries  are  opening  up  that 
there  is  no  fear  that  science  will  yet  awhile 
be  sighing,  like  Alexander,  for  fresh  worlds 
to  conquer. 


PHYSICAL  HISTORY  19 

Before  the  doctrine  of  its  conservation  was 
established,  energy  was  mysterious  and  un- 
accountable in  its  comings  and  goings. 
To-day  it  is  no  longer  a  mystery.  The 
unaccounted-for  appearance  or  disappearance 
of  a  quantity  of  energy  in  any  process,  how- 
ever complex,  would  rouse  as  much  scientific 
interest  as  the  mysterious  appearance  or 
disappearance  of  matter.  When  it  appears 
it  must  come  from  somewhere,  and  when  it 
disappears  it  must  go  somewhere.  Gradually 
this  Law  of  Conservation  has  supplied  the 
physicist  with  an  experimental  test  of  reality 
in  a  changing  universe.  What  appears  and 
disappears  mysteriously,  giving  no  clue  of 
its  origin  or  destination,  is  outside  of  his 
province.  To  him  it  has  no  physical  exist- 
ence. What  is  conserved  has  physical 
existence,  whether  it  is  tangible  and  ponder- 
able like  matter,  or  intangible  and  imponder- 
able like  energy.  Early  writers,  when  they 
really  meant  what  is  now  called  energy,  often 
used  the  term  force;  and  the  idea  of  force,  as 
will  later  be  discussed,  has  confused  the  issues 
and  retarded  the  growth  of  science  to  an  al- 
most incalculable  extent.  Carlyle  says, 
meaning  energy — "Force,  force,  everywhere 
Force;  we  ourselves  a  mysterious  Force  in 
the  centre  of  that  'There  is  not  a  leaf  rotting 


*0  MATTER  AND  ENERGY 

on  the  highway  but  has  Force  in  it:  how  else 
could  it  rot?'"  The  very  idea  of  Force  is, 
however,  what  would  be  termed  an  anthro- 
pomorphism, that  is  to  say,  it  ascribes  the 
behaviour  of  inanimate  objects  to  causes 
derived  from  the  behaviour  of  human  beings. 
We  have  come  to  associate  the  motion  of 
matter  with  somebody  or  something  pulling 
or  pushing  it.  When  one  body  is  observed  to 
move  towards  another,  like  a  stone  falling  to 
the  ground,  it  has  been  supposed  that,  al- 
though no  agent  is  visible,  something  must 
be  pulling  it.  What,  however,  is  actually 
observed  is  a  change  of  position  of  the  body, 
which  acquires  at  the  same  time  motion  or 
velocity.  The  observation  is  correctly  ex- 
pressed by  saying  that  energy,  before  asso- 
ciated with  the  position  of  one  body  with 
reference  to  another  (potential  energy),  has 
changed  into  energy  of  motion  (kinetic 
energy).  To  suppose  that  the  one  body 
attracts  or  pulls  the  other  with  a  certain 
"force"  is  to  imagine  a  cause,  which  if  it 
existed  would  account  for  the  effect.  Forces 
are  not  conserved,  they  have  no  physical 
existence,  but  they  still  survive  even  in 
scientific  parlance,  mainly  because  of  the 
poverty  of  the  language,  which  hardly  allows 
effects  to  be  expressed  without  some  causal 


PHYSICAL  HISTORY  21 

inference.  They  are  bad  gates  through 
which  to  approach  the  study  of  energy,  as 
is  evident  from  the  fact  that  mechanics 
existed  in  a  highly  developed  state  for  cen- 
turies before  the  discovery  of  the  conserva- 
tion of  energy.  In  mechanics,  which  is  the 
science  of  the  motion  or  absence  of  motion 
of  matter  in  bulk,  forces  have  a  definite 
meaning,  and  in  terms  of  energy  they  are 
measured  by  the  change  in  the  kinetic  (or 
potential)  energy  of  a  body  when  its  position 
changes  by  the  unit  of  length.  Many  of  the 
most  important  changes  of  energy  are  due  to 
changes  of  position,  too  small  to  be  measur- 
able, between  the  smallest  particles  of  the 
substance.  The  energy  changes  are,  however, 
easily  measurable.  The  attempt  even  to 
imagine  forces  to  exist  in  such  cases  as  the 
causes  of  the  changes  of  energy,  in  absence 
of  all  knowledge,  not  only  of  the  actual 
distances  involved  but  also  of  the  variation 
of  the  imagined  cause  with  the  distance,  is 
to  invent  an  elaborate,  perfectly  vague  and 
befogging  mode  of  expression  for  a  very  simple 
effect.  It  is  better  to  try  to  grasp  the  meaning 
of  energy  as  a  fundamental  fact  of  experience 
than  to  begin,  with  totally  inadequate  knowl- 
edge, to  derive  from  the  action  of  living 
beings  a  shallow  analogy  which,  if  true, 


22  MATTER  AND  ENERGY 

would  serve  as  a  possible  explanation  of  a 
few  of  the  grosser  manifestations  in  which 
energy  plays  a  part. 

Energy  is  recognised  in  two  forms,  kinetic 
and  potential.  The  first  depends  on  motion, 
the  second  on  the  position  of  the  body  under 
consideration,  and  the  law  of  conservation 
states  that  any  loss  of  energy  of  motion  is 
balanced  by  a  gain  due  to  position,  and  vice 
versa.  But  it  is  possible  to  select  cases  in 
which  the  distribution  of  the  kinetic  energy 
changes,  as  among  various  moving  bodies, 
without  any  abiding  changes  of  potential 
energy.  The  effect  of  position  can  thus  be 
eliminated,  and  the  question  reduced  to  its 
simplest  form.  The  law  of  conservation, 
then,  has  reference  simply  to  kinetic  energy 
or  energy  of  motion.  The  question  that 
first  has  to  be  asked  is,  What  is  conserved? 
Neither  motion  as  such,  nor  what  Newton 
termed  quantity  of  motion,  or  momentum, 
the  product  of  the  mass  of  the  moving  body 
and  its  velocity,  is  conserved.  A  sufficiently 
good  example  is  in  the  collision  of  two  elastic 
balls.  No  material  is  perfectly  elastic,  it 
is  true,  and  in  all  actual  collisions  some  of 
the  energy  of  motion  of  the  body  as  a  whole 
is  transformed  into  heat,  or  the  energy  of 
motion  of  its  smallest  parts  with  reference  to 


PHYSICAL  HISTORY  23 

one  another.  This  part  can  be  accurately 
measured  in  practice,  so  that  for  the  purposes 
of  a  simple  illustration  it  is  legitimate  to 
consider  the  balls  chosen  as  perfectly  elastic, 
colliding  on  a  level  plane — for  example,  a 
billiard  table.  If  two  perfectly  elastic  balls 
collide,  no  matter  what  the  relative  masses 
of  the  balls,  or  what  their  relative  velocities, 
there  is  only  one  quantity,  involving  these 
masses  and  velocities,  which  is  the  same 
before  and  after  the  collision.  That  quantity 
is  the  sum  obtained  by  adding  together  the 
product  of  the  mass  of  each  ball  and  the 
square  of  its  velocity.  The  measure  of 
kinetic  energy  adopted  is  half  the  mass 
multiplied  by  the  square  of  the  velocity. 
The  numerical  factor  one-half  is  not  of  great 
significance  in  the  present  connection.  The 
important  fact  is  that  it  is  the  square  of  the 
velocity  and  not  the  velocity  itself  which  is 
conserved.  It  is  the  same  in  the  case  of  all 
phenomena  in  which  pure  motion  uninfluenced 
in  any  lasting  way  by  position  is  considered. 
No  matter  what  changes  have  occurred  in  the 
relative  motions  of  the  moving  parts,  the 
sum  of  the  products  of  the  masses  into  the 
square  of  their  velocities  is  conserved.  This 
therefore  answers  the  question  as  to  how 
kinetic  energy  depends  on  motion.  It  might 


24  MATTER  AND  ENERGY 

be  supposed  that  a  truth  deduced  thus  halt- 
ingly from  the  behaviour  of  imaginary  per- 
fectly elastic  substances  had  no  very  great 
application  in  the  real  world.  As  a  matter  of 
fact,  it  is  what  we  call  imperfect  elasticity 
which  has  no  great  range  of  application  in 
the  real  world,  the  world  of  molecules,  as 
contrasted  with  the  gross  world  of  matter 
in  bulk,  which  is  all  our  unaided  senses  can 
perceive.  The  application  of  the  principle 
to  all  cases  of  pure  motion  is  universal,  and 
the  reservation  as  to  imperfect  elasticity 
had  to  be  made  simply  because  it  is  not 
immediately  obvious  that  loss  of  kinetic 
energy  of  motion  and  its  transformation 
into  heat  is  merely  subdivision  of  motion 
among  smaller  particles  of  matter  that  can 
be  directly  perceived.  Molecules,  if  they  are 
really  the  smallest  particles  of  matter  that 
exist,  must  be  perfectly  elastic,  as  later  on 
will  be  quite  evident.  It  would  be  as  absurd 
to  postulate  an  inelastic  molecule  in  pure 
science,  as  it  is  at  present  understood,  as  it 
would  be  to  assume  for  the  motion  of  each 
individual  in  a  surging  crowd  the  general 
chaotic  aimlessness  which  appears  to  char- 
acterise the  whole.  The  science  of  heat  is 
mainly  one  grand  general  example  of  the  very 
case  that  has  been  postulated,  namely,  that  of 


PHYSICAL  HISTORY  25 

pure  motion  uninfluenced  by  position,  not 
in  the  visible  seeming  world  of  gross  masses, 
but  in  the  invisible  real  world  of  molecules. 

In  physics,  work  and  energy  are  inter- 
changeable terms.  The  simplest  case  of 
doing  work  is  the  lifting  of  a  weight  from 
the  ground  to  a  height.  The  amount  of  work 
done,  and  the  amount  of  energy  spent  in 
doing  it,  are  simply  proportional,  first,  to  the 
mass  or  quantity  of  the  matter  lifted;  second, 
to  the  height  it  is  lifted.  Mass  is  practically 
measured  by  weight,  so  long  as  the  measure- 
ments refer  to  one  part  of  the  earth.  Owing 
to  the  fact  that  the  position  of  an  object  on 
the  surface  of  the  earth  relative  to  its  centre 
varies  with  the  latitude,  the  distance  apart 
being  appreciably  greater  at  the  equator 
than  at  the  poles,  a  given  mass  weighs  slightly 
less,  and  falls  to  the  ground  a  little  less 
rapidly,  in  the  tropics  than  elsewhere.  What 
follows  refers  to  a  single  locality  where  weight 
is  truly  a  measure  of  mass.  It  does  not  require 
any  appreciably  different  amount  of  work  to 
lift  a  weight  in  the  upper  room  of  a  house  than 
in  the  basement.  When  a  weight  is  lifted, 
kinetic  energy  disappears  and  the  equivalent 
quantity  of  potential  energy,  measured  by 
the  weight  of  matter  multiplied  by  the 
height  it  is  lifted,  is  produced.  A  foot- 


26  MATTER  AND  ENERGY 

pound  is  one  unit  of  potential  energy  due  to 
height.  Twenty  foot-pounds  is  practically  the 
same  whether  it  refers  to  the  work  done  on  a 
20  Ib.  weight  raised  one  foot,  or  on  a  1  Ib. 
weight  raised  20  feet.  When  the  weight 
falls  again,  the  potential  energy  disappears 
and  the  equivalent  quantity  of  kinetic  energy, 
measured  by  half  the  mass  of  matter  multi- 
plied by  the  square  of  the  velocity  it  acquires 
at  the  end  of  its  descent,  reappears.  The 
truth  of  the  statement,  derived  from  experi- 
mental observation,  that  it  is  the  square  of 
the  velocity,  not  the  velocity  itself,  which  is  a 
measure  of  the  kinetic  energy,  may  now  be 
made  a  little  more  obvious.  The  kinetic 
energy  acquired  by  a  falling  weight  is  the 
equivalent  of  the  potential  energy  it  possessed 
prior  to  falling,  and  is  therefore  the  product 
of  the  weight  and  the  height  of  fall.  If 
kinetic  energy  were  proportional  to  the 
velocity  simply,  just  as  potential  energy  is 
proportional  to  the  height,  it  would  follow, 
therefore,  that  the  velocity  of  a  falling  body 
should  increase  uniformly  with  the  height  it 
falls.  Whereas  the  velocity  increases,  as 
every  one  knows,  uniformly  with  the  time 
taken  for  the  fall.  As  the  speed  gets  faster 
and  faster  a  greater  distance  is  traversed  in 
each  succeeding  second,  and  therefore  for 


PHYSICAL  HISTORY  27 

each  succeeding  foot  fallen  through  the 
velocity  must  increase  by  a  less  and  less 
amount.  The  velocity  acquired  is  propor- 
tional not  to  the  height,  but  to  the  square 
root  of  the  height  of  fall.  The  kinetic  energy 
acquired  is  proportional  to  the  height,  and 
must  therefore  increase  according  to  the 
square  of  the  velocity.  If  further  illustra- 
tion were  needed  that  the  kinetic  energy 
acquired  by  a  falling  body  is  proportional 
simply  to  the  height  of  the  fall,  all  that  is 
necessary  is  to  carry  out  the  fall  in  two 
equal  stages.  The  body  falls  the  same 
height  in  each  stage,  and  therefore  acquires 
the  same  velocity  and  kinetic  energy.  But 
in  falling  the  whole  way  the  velocity  acquired 
is  not  twice  that  acquired  in  falling  half-way, 
but  the  square  root  of  twice.  The  law  of 
dependence  of  kinetic  energy  on  motion  can 
thus  be  deduced  from  the  observed  laws  of 
falling  bodies. 

Space  does  not  permit  more  than  a  refer- 
ence to  the  early  history  of  the  doctrine  of 
energy.  The  first  conception  had  reference 
to  chemical  energy,  and  was  contained  in 
the  Theory  of  Phlogiston  which  dominated 
chemistry  during  the  eighteenth  century. 
The  twin  laws  of  conservation,  that  of  matter 
and  of  energy,  struggled  competitively  for 


28  MATTER  AND  ENERGY 

birth  in  the  search  of  science  after  the  un- 
changing entities.  Energy  was  always  being 
confounded  with  matter.  Even  the  great 
chemist  Boyle,  who  gave  us  the  modern 
conception  of  elements,  thought  that  heat 
was  ponderable.  The  search  was  intuitively 
after  conservation,  and  matter  was  less 
elusive  than  energy.  Hence  everything  in- 
tuitively believed  to  be  real  ran  the  risk  of 
being  regarded  as  material.  This  was  the 
fate  of  phlogiston.  As  first  put  forward, 
phlogiston  was  something  which  escaped 
during  fire,  or  combustion,  with  the  light 
and  heat  evolved.  It  was  a  pure  anticipation 
of  what  is  now  called  energy.  Combustible 
substances  were  regarded  as  rich  in  phlogis- 
ton. The  lode-star  of  conservation  appeared 
first  in  the  following  way.  When  various  prod- 
ucts of  processes,  which  were  recognised  as 
being  analogous  to  combustion,  like  the 
calces,  or  as  we  should  say  oxides,  of  the 
metals,  or  sulphuric  acid  and  the  sulphates, 
were  heated  with  highly  inflammable  bodies 
like  coal,  oil,  or  organic  matter,  the  original 
combustible  substances,  that  is,  the  metals 
or  the  sulphur,  as  the  case  might  be,  were 
regenerated.  This  view  recognised  that  dur- 
ing combustion  something  (energy),  which 
manifested  itself  as  light  and  heat,  escaped; 


PHYSICAL  HISTORY  29 

and  that,  before  the  original  materials  could 
be  got  back  from  the  products  of  combustion, 
this  something  had  to  be  put  back.  It  was 
only  recognised  much  later  that  during  com- 
bustion something  material  (oxygen)  was 
absorbed  from  the  air,  and  that  before  the 
products  could  be  regenerated  the  compound 
formed  had  to  be  decomposed  and  the 
oxygen  liberated.  The  spirit  of  chemistry 
tended  towards  pure  materialism.  The  later 
followers  of  the  phlogiston  theory  made  the 
fatal  mistake  of  materialising  phlogiston. 
With  the  enthronement  of  the  balance,  and 
the  test  of  weight  as  the  criterion  of  material 
reality,  the  existence  of  phlogiston  as  a 
material  substance  was  disproved,  and  the 
theory  itself  fell  into  quite  undeserved  dis- 
repute. In  its  original  form  it  anticipated 
by  more  than  a  century  the  modern  doctrine 
of  energy.  It  is  most  wonderful  to  reflect 
that  the  first  idea  of  conservation  in  science 
arose  not  in  connection  with  weighable 
matter,  but  with  the  elusive,  imponderable 
energy.  The  second  or  modern  phase  arose 
in  connection  with  the  nature  of  heat,  after 
the  law  of  the  conservation  of  matter  had 
been  established,  when  it  was  no  longer 
possible  to  regard  heat  as  a  material  fluid. 
Davy  and  Rumford,  at  the  commencement 


30  MATTER  AND  ENERGY 

of  last  century,  both  had  the  modern  con- 
ception of  heat  as  a  mode  of  motion  of 
matter,  and  both  came  very  near  to  estab- 
lishing it.  The  latter  was  engaged  in  the 
boring  of  cannon  by  means  of  horses,  and 
observed  the  large  amount  of  heat  con- 
tinuously generated  during  the  operation. 
He  records  in  one  experiment  that  by  the 
work  of  a  single  horse  19  Ibs.  of  water  were 
boiled,  and  the  cannon,  drill,  and  all  the 
machinery  employed  were  heated  up  to  the 
boiling  point  of  water  in  140  minutes.  But 
boring  changes  the  state  of  the  metal  from 
the  compact  to  the  finely  divided  form  of 
borings  and  turnings,  and  it  had  to  be  proved 
that  the  latter  had  not  a  less  capacity  for 
heat  than  the  former.  Joule,  who  repeated 
the  experiments  in  another  form  by  merely 
churning  water,  which  suffers  thereby  no 
physical  change  except  rise  of  temperature, 
established  the  modern  view  that  the  source 
of  the  heat  is  in  the  power  or  energy  ex- 
pended. He  measured  exactly  how  much 
heat  is  produced  by  a  given  amount  of 
mechanical  work,  and  found  that  772  foot- 
pounds have  to  be  spent  to  raise  the  tempera- 
ture of  1  Ib.  of  water  1°  Fahrenheit.  The 
water  of  a  waterfall,  772  feet  high,  tumbling 
over  into  a  deep  pool,  so  that  practically 


PHYSICAL  HISTORY  31 

all  of  its  kinetic  energy  is  converted  into 
heat,  is  1°  F.  hotter  at  the  bottom  than  at 
the  top.  Expressed  in  the  modern  scientific 
units,  which  are  based  on  the  gram  (.035  oz. 
or  15.4  grains)  as  the  unit  of  mass,  the  centi- 
metre (0.394  inch)  as  the  unit  of  length,  and 
the  second  as  the  unit  of  time,  Joule's  equiva- 
lent is  42,650.  That  is,  a  weight  of  42.65 
kilograms  falling  a  centimetre  has  sufficient 
energy  to  raise  the  temperature  of  1  gram 
of  water  1°  Centigrade.  The  latter  unit  of 
heat  is  known  as  the  caloric.  In  the  com- 
bustion of  coal,  considered  as  pure  carbon, 
the  heat  evolved  would  raise  the  temperature 
of  a  mass  of  water  about  8000  times  that  of 
the  coal  1°  Centigrade,  or  a  mass  14,000  times 
1°  Fahrenheit. 

Conversely,  when  work  is  produced  by  any 
heat  engine  the  equivalent  quantity  of  heat 
disappears.  As  is  well  known,  the  conversion 
of  heat  into  mechanical  work  is  a  very  waste- 
ful process.  But  if  it  were  possible  to  convert 
the  chemical  energy  of  coal  completely  into 
work,  without  first  burning  it  to  liberate  the 
energy  as  heat,  the  energy  of  1  ton  of  coal 
would  then  be  sufficient  to  lift  one  of  the 
largest  liners,  weighing  20,000  tons,  500 
feet  high.  In  other  words,  the  chemical 
energy  of  coal  is  equivalent  to  that  of  a 


32  MATTER  AND  ENERGY 

mass  equal  to  the  mass  of  the  coal  falling 
under  gravity  a  distance  of  2000  miles,  or 
one  quarter  of  the  earth's  diameter.  The 
engineer's  unit — the  horse-power — denned 
after  actual  tests  with  the  best  British  cart- 
horses, is  a  rate  at  which  work  is  done  or 
energy  is  spent.  One  horse-power  will  lift 
a  weight  of  550  Ib.  one  foot  per  second.  A 
horse-power-hour,  or  one  horse-power  acting 
for  a  period  of  6ne  hour,  is  thus  almost  exactly 
two  million  foot-pounds.  The  "Board  of 
Trade  Unit,"  at  which  electrical  power  is 
supplied  to  consumers,  is  the  "Kilowatt- 
hour,"  and  is  about  a  third  greater  than  the 
horse-power-hour.  This  is  the  energy  con- 
sumed by  an  ordinary  4-lamp  electric  radiator 
in  an  hour,  but  if  converted  into  mechanical 
energy  instead  of  heat  it  would  raise  a  weight 
of  1  ton,  1200  feet  high. 

The  Apostle  Paul  had  no  thought  of 
physical  things  in  his  mind  when  he  used  the 
words,  "The  things  which  are  seen  are  tem- 
poral, but  the  things  which  are  not  seen  are 
eternal."  But  the  words  can  be  applied  with 
profit  to  illustrate,  perhaps  more  forcibly 
than  any  single  sentence,  the  essential  nature 
of  energy.  It  is  only  the  temporary  changes 
in  the  form  and  relative  amount  of  energy 
which  are  manifest.  So  long  as  energy 


PHYSICAL  HISTORY  33 

neither  changes  in  amount  nor  position  in 
space,  it  belongs  to  the  unseen  and  eternal. 
No  direct  evidence  of  its  existence  can  be 
obtained.  It  is  true  that,  if  in  similar  cases 
changes  in  the  energy  have  occurred,  the 
existence  of  the  energy  may  be  deduced 
from  analogy.  Thus  so  long  as  nitroglycerin 
or  guncotton  do  not  suffer  changes  there  is  no 
possible  way  of  measuring  or  recognising  the 
energy  they  contain,  though  from  the  observa- 
tion that,  in  previous  cases,  such  substances 
have  under  certain  conditions  invariably 
been  found  suddenly  to  evolve  a  large  amount 
of  energy,  suffering  at  the  same  time  complete 
change  of  material  character,  the  existence 
of  the  energy  may  be  inferred  with  certainty. 
The  total  energy  contained  in  matter  depends 
upon  the  extent  to  which  it  can  be  changed. 
When  it  has  been  pulled  to  pieces  and  its 
smallest  component  parts  dispersed  out  of 
the  range  of  one  another's  influence,  the 
difference  between  the  energy  initially  and 
finally  present  can  be  found.  The  absolute 
value  of  potential  energy  involves  a  complete 
knowledge  of  the  real,  as  contrasted  with  the 
so  far  attained,  limits  of  subdivision  of 
materials.  The  absolute  value  of  kinetic 
energy  involves  a  knowledge  of  the  real  or 
absolute  velocity  of  the  moving  body,  as 


84  MATTER  AND  ENERGY 

contrasted  with  the  motion  relative  to  the 
earth,  which  is  all  that  usually  has  to  be  taken 
into  account. 

But  the  fact  that  the  energy  resources  of 
Nature  may  be  practically  limitless  does  not 
in  the  least  affect  the  way  the  accounts  are 
kept,  or  the  amount  that  can  be  derived  for 
practical  purposes.  This  amount  ultimately 
controls  the  number  of  people  the  world  can 
support,  and  the  intensity  of  their  struggle 
for  existence.  The  discovery  of  a  large 
quantity  of  gold  leaves  the  world  not  a  penny 
the  richer.  Those  that  find  it  are,  by  con- 
vention, made  wealthy  at  the  public  expense. 
In  addition,  if  gold  increases  in  abundance 
without  a  corresponding  increase  in  pros- 
perity, the  purchasing  power  of  money 
diminishes,  prices  of  all  commodities  rise,  and 
long  and  bitter  industrial  strife  results 
between  the  wage-earner  and  the  employer. 
But  energy  and  wealth  are  synonymous. 
Energy  is  the  thing  of  which  gold  itself  is 
but  the  guinea  stamp,  to  adapt  the  simile  of 
Burns.  A  find  of  energy  in  Nature  means  an 
addition  to  the  general  wealth,  a  postpone- 
ment of  the  day  of  bankruptcy,  which  each 
new  invention  of  science,  on  the  other  hand, 
brings  nearer.  Physical  history,  the  science 
of  the  physical  conditions  underlying  the 


PHYSICAL  HISTORY  35 

past,  present,  and  future  history  of  the  race, 
has  some  rude  disillusionments  in  store. 
It  was  not  so  very  long  ago  that  a  Member 
of  Parliament  condoned  the  wasteful  methods 
of  utilising  coal  on  the  ground  of  the  addi- 
tional benefit  that  accrued  thereby  to  the 
coal  industry.  At  the  moment  of  writing, 
employers  and  employed  in  that  industry 
are  calmly  contemplating  a  complete  stoppage 
while  they  fight  out  their  differences,  and  the 
public  experiences  a  temporary  return  to 
the  original  conditions  of  life  of  primitive 
man.  It  is  curious  that  it  should  have  taken 
so  long  for  the  age  to  realise  that  it  differs 
physically  and  fundamentally  from  all  the 
preceding  eras  of  history  only  in  the  utilisa- 
tion of  the  energy  of  fuel.  The  ignorance 
and  apathy  of  the  ancients  in  reference  to 
the  metals,  the  mastery  over  which  distin- 
guished them  from  their  predecessors,  is 
paralleled  by  the  situation  to-day  with 
regard  to  this  new  life-blood  of  civilisation. 
The  horror  of  the  waste  of  food  is  inborn,  the 
horror  of  the  waste  of  fuel  has  still  to  be 
acquired. 

Let  us  spend  a  few  moments  in  examining 
critically  the  conditions  of  the  existence  of 
the  present  age  of  energy.  What  is  this 
coal,  which  is  rated  so  lightly  as  a  mere  com- 


36  MATTER  AND  ENERGY 

modity,  to  be  bought  and  sold,  wasted  or 
utilised,  as  much  or  as  little  as  individuals 
think  fit?  As  commonly  regarded,  it  is  a 
substance  which,  by  indomitable  industry, 
perseverance,  and  pluck,  man  succeeds  in 
digging  up  from  the  bowels  of  the  earth. 
The  enterprise  and  expansion  of  the  world, 
consequent  upon  an  abundant  coal  supply, 
are  regarded  as  the  just  return  of  human 
effort  and  expenditure.  Its  market  price, 
at  the  pit's  head,  of  so  many  shillings  per  ton, 
represents  the  cost  of  bringing  it  to  the 
surface,  just  as  its  price  in  a  locality  remote 
from  the  mine  represents  this  cost  together 
with  the  cost  of  transportation.  Not  a 
thought  is  given  as  to  what  the  coal  has  cost 
Nature.  Science  regards  coal  in  a,  different 
light,  as  a  legacy  from  the  bygone  past, 
which  man,  having  attained  his  majority 
and  acquired  a  knowledge  of  its  utilisation, 
is  engaged  in  spending  and  dissipating  as 
fast  as  it  can  be  brought  to  the  surface.  The 
cost  at  the  pit's  head  no  more  has  any  relation 
to  the  real  value  of  the  coal  than  the  cost 
of  its  transport  above  the  ground.  The  only 
part  of  its  value  for  which  any  return  is 
demanded  is  the  cost  of  transportation  from 
the  place  where  it  occurs  to  the  place  where 
it  is  used.  The  coal  itself  represents  the 


PHYSICAL  HISTORY  37 

accumulation  of  solar  energy  over  almost 
incredible  periods  of  time.  The  primaeval 
forests  of  the  carboniferous  era  were  not, 
the  geologists  tell  us,  mushroom  growths. 
The  layers  of  shale  between  each  shallow 
seam  indicate  that,  alternately,  the  site  of 
the  forest  was  dry  land  and  the  bed  of  the 
sea.  For  the  formation  even  of  a  single 
seam,  alterations  of  the  contour  of  land  and 
sea  must  have  occurred  which  require  not 
years  nor  lifetimes,  but  geological  epochs. 
It  is  not  possible  to  reckon  what  the  cost  of 
coal  has  been  in  the  economy  of  Nature,  nor 
how  many  ages  of  future  time  will  be  neces- 
sary to  recuperate  the  amount  now  burned  in 
a  single  year.  On  this  irreplaceable  and 
diminishing  commodity  the  future  prospects 
of  civilisation  depend.  Primitive  races  were 
dependent  entirely  on  the  regular  day  to  day 
supply  of  natural  energy,  and  were  imperilled 
by  each  temporary  failure  or  diversion  of  the 
supply.  All  that  civilisation  has  yet  con- 
trived is  to  augment  the  natural  supplies  out 
of  capital,  under  the  delusion  that  it  was 
supporting  itself  out  of  income  on  a  more 
liberal  scale  than  its  predecessors,  because  of 
the  greater  scope  of  its  knowledge  and  in- 
tellectual powers!  It  is  a  pure  delusion. 
The  knowledge  which  shall  provide  as  well  as 


38  MATTER  AND  ENERGY 

spend,  and  which  shall  place  civilisation  upon 
the  broad  flowing  river  of  energy,  which 
supplies  the  vast  requirements  of  the  universe 
over  infinite  periods  of  time,  is  not  yet  born. 
The  age  in  which  we  live,  the  age  of  coal, 
draws  its  vivifying  stream  from  a  dwindling 
puddle  left  between  the  comings  and  goings 
of  the  cosmical  tide. 


CHAPTER  II 

MATTER:  i.  ATOMS  AND  MOLECULES 

WE  possess  five  senses  by  means  of  which 
the  mind  makes  its  acquaintance  with  the 
external  world.  Possibly  the  mind  has  other 
channels  of  communication  not  comprised 
within  the  five  senses;  but  if  so,  they  have  not 
yet  come  within  the  scope  of  science.  In 
the  history  of  the  science  of  matter  two  main 
types  of  mind  can,  in  general,  be  distin- 
guished, one  of  which  has  developed  into  the 
modern  type  of  scientific  mind,  although  the 
other  type  is  by  no  means  non-existent.  The 
two  types  may  be  illustrated  by  the  ancient 
and  modern  conception  of  elements.  TJie 
word  element  is  possibly  derived  from  the 
letters  I  m  n  of  the  alphabet,  conveying  the 


MATTER:  I.  ATOMS  39 

idea  that  material  things  were  built  up  of 
elements  as  a  word  is  built  up  of  letters. 
But  the  ancient  and  modern  ideas  of  these 
fundamental  things  called  elements  were 
entirely  different.  The  older  type  of  mind 
regarded  all  the  forms  of  matter  as  a  com- 
bination of  certain  elementary  qualities, 
the  newer  type  as  a  combination  of  certain 
elementary  substances. 

There  seems  to  have  been  distinguished  by 
the  Greek  mind  two  fundamental  qualities 
and  their  opposites,  the  one  Dryness,  the 
other  Hotness,  with  their  opposites  Wetness 
and  Coldness.  These  four  qualities  were 
combined  in  pairs  to  make  the  four  "Ele- 
ments," Earth,  Air,  Fire,  and  Water.  "  Fire  " 
was  Hotness  combined  with  Dryness; 
"Earth,"  Coldness  and  Dryness;  "Water," 
Coldness  and  Wetness;  "Air,"  Hotness  and 
Wetness.  These  so-called  elements  had  no 
relation  to  the  actual  things  called  earth, 
air,  fire,  and  water  beyond  the  fact  that  the 
ancients  considered  the  actual  things  typical 
examples  of  all  the  possible  combinations 
of  the  qualities  they  thought  most  funda- 
mental. Probably  many  have  puzzled  them- 
selves over  the  meaning  of  the  "four  Ele- 
ments," Earth,  Air,  Fire,  and  Water.  They 
are  scarcely  worth  it.  The  type  of  mind 


40  MATTER  AND  ENERGY 

which  created  the  four  Elements  was  in  the 
ascendant  all  through  the  Dark  Ages,  and 
as  a  direct  consequence  arose  Alchemy — the 
beginnings  of  Chemistry.  If  the  qualities  of 
things  are  regarded  as  more  fundamental 
than  the  things  themselves;  or  if  things  are 
looked  upon  as  having  no  existence  apart 
from  the  qualities  which  they  possess,  the 
transmutation  of  one  element  into  another 
appears  very  much  the  same  as  any  other 
kind  of  chemical  change.  The  ancients  were 
acquainted  with  brass,  and  with  the  manner 
of  its  production  by  heating  copper  with 
ores  of  Zinc.  Here  we  have  a  case,  they 
might  argue,  where  one  of  the  qualities  of 
copper,  namely,  its  colour,  has  been  changed 
into  that  of  gold.  This  is  the  first  step  in 
the  transmutation  of  copper  into  gold.  Why 
should  it  not  be  possible,  one  at  a  time,  to 
change  each  property  of  copper,  in  the  same 
way  as  its  colour,  so  as  ultimately  to  arrive 
at  a  substance  having  all  the  qualities  of 
gold?  On  their  philosophy  brass  was  gold 
so  far  as  its  colour  went,  not,  as  we  should 
say,  like  it. 

The  modern  habit  of  thought  recognises 
things  as  having  a  real  existence  apart  alto- 
gether from  the  particular  qualities  or  prop- 
erties by  means  of  which  the  things  make 


MATTER:  I.  ATOMS  41 

themselves  known  to  the  five  senses.  The 
acceptance  of  this  habit  of  thought  among 
scientific  men  has  been  due  mainly,  not  to 
any  formal  proof,  but  to  its  fertility  and  to 
the  undoubted  value  of  the  results  which 
follow  from  it.  Deep  down  somewhere  in 
the  processes  of  thought  the  ultimate  test 
of  reality  appears  to  be  the  Law  of  Conserva- 
tion. Does  the  soul  exist?  If  so,  it  must 
be  immortal.  Is  matter  real  or  a  mere 
impression  of  the  mind?  It  cannot  be 
created  or  destroyed,  and  therefore  has  an 
existence  apart  from  the  mind.  Lastly,  has 
energy  a  specific  existence,  or  is  it  merely  a 
convenient  abstraction?  Energy  is  con- 
served like  matter,  and  therefore  obeys  this 
test  of  objective  existence.  Now  consider 
the  essential  quality  of  all  the  phenomena 
of  the  occult  world — apparitions,  ghosts, 
spirits,  astral  bodies,  and  so  on.  It  is  that 
they  are  not  conserved.  They  appear  no 
one  knows  whence,  and  they  disappear  no 
one  knows  whither.  They  do  not  obey  this 
test  of  reality,  and  the  doubt  remains  how 
far  they  exist  apart  from  the  brain  which 
apprehends  them.  It  would  ill  become 
science  to  deny  the  reality  of  things  with 
which  it  has  no  concern.  But  it  has  most 
definitely,  but  at  the  same  time  unconsciously, 


42  MATTER  AND  ENERGY 

limited  itself  till  now  to  the  recognition  of 
only  those  existences  which  appear  to  obey 
the  Law  of  Conservation,  and  for  which, 
therefore,  there  is  this  much  of  proof  of 
reality. 

What,  then,  are  the  fundamental  existences 
recognised  by  physical  science?  Probably 
there  are  at  least  three: — Matter,  Electricity, 
and  Energy.  The  commonest  questions  ever 
asked  are— "What  is  Matter?"  "What  is 
Electricity?"  "What  is  Energy?"  The 
questions  reveal  the  intuitive  method  of  the 
human  mind  in  approaching  Nature — the 
attempt  to  explain  things  not  understood  in 
terms  of  things  simpler  and  more  funda- 
mental. Obviously,  however,  it  cannot  be 
applied  to  the  most  fundamental  conceptions 
themselves.  To  be  asked  to  define  or  explain 
a  fundamental  entity  is  to  be  asked  to  explain 
bricks  in  terms  of  houses.  It  is  just  because 
science  has  asked  these  questions  over  and 
over  again  without  getting  an  answer  that 
the  existence  of  these  three  things  is  con- 
sidered fundamental.  A  legitimate  question 
would  be,  "How  is  a  thunderstorm  explained 
in  terms  of  electricity,  matter,  and  energy?" 
But  to  ask  this  question,  "What  is  Matter?" 
is  to  assume  that  there  exists  something  more 
simple  and  fundamental  than  matter,  out  of 


MATTER:  I.  ATOMS  43 

which  it  is  in  some  way  made  up.  There 
may  be,  but  if  so  it  is  not  yet  completely 
known.  We  make  up  our  minds,  therefore, 
to  accept  the  existence  of  as  few  fundamental 
things  as  possible  which  cannot  be  explained 
in  terms  of  anything  else.  When  it  becomes 
possible  to  say  exactly  what  they  are,  they 
will  no  longer  be  fundamental,  but  there 
always  must  be  a  certain  number  of  funda- 
mental things  not  explainable  in  terms  of 
anything  else,  representing  the  limits  to 
which  the  analysis  of  phenomena  has  been 
reduced. 

Now  the  human  mind  intuitively  believes 
that  there  are  very  few  fundamental  things 
in  this  sense,  and  if  experience  shows  that 
there  are  more,  it  is  apt  to  anticipate  future 
discovery  by  assuming  the  complexity  of 
what  has  to  be  regarded  strictly  as  funda- 
mental. This  is  precisely  the  case  with 
matter.  So  far  matter  has  been  referred  to 
as  one  of  the  fundamental  existences,  and  it 
has  been  tactily  assumed  that  all  matter  is 
made  up  of  various  combinations  of  the  same 
unknown  "primary  stuff"  or  "protyle." 
As  a  matter  of  fact,  before  the  discovery  of 
radioactivity,  no  less  than  eighty  elements 
were  known,  none  of  which  could  be  formed 
from  or  turned  into  any  other,  and  each  was 


44  MATTER  AND  ENERGY 

therefore  a  fundamental  form  of  matter, 
having  a  separate  existence.  Just  as  at 
present  it  would  be  futile  to  ask  what  is 
matter,  so  it  would  be  to  ask  what  is  gold,  or 
copper,  or  any  other  of  the  eighty  elements. 
Each  is  a  separate  and  distinct  thing,  and 
has  to  be  accepted  as  such.  All  its  prop- 
erties may  be  learnt,  studied,  and  classified, 
but  not  one  can  be  explained. 

Every  known  material  thing  in  the  universe 
may  be  regarded  as  composed  of  one  or 
more  of  these  elements  in  definite  quantities, 
capable  of  being  analysed  or  decomposed 
into  its  several  constituent  elements,  and 
often  of  being  re-formed  from  them.  The 
complicated  materials  making  up  the  bodies 
of  living  beings  are  easy  to  decompose  into 
their  constituent  elements,  but  only  in  certain 
cases  have  they  been  built  up  artificially  or 
"synthesised"  directly  from  the  elements. 
By  far  the  greater  number  of  the  important 
products  of  the  vegetable  world  have  now 
been  synthesised,  one  of  the  more  recent 
being  camphor,  which  engaged  the  attention 
of  numerous  chemists  for  many  years  before 
it  was  artificially  prepared.  The  synthetical 
production  of  rubber  has  long  been  known. 
Often,  however,  it  is  immensely  more  costly 
to  make  the  products  artificially  than  to  grow 


MATTER:  I.  ATOMS  45 

them,  so  that  it  must  not  be  supposed  that 
the  synthesis  of  any  commodity  means  the 
immediate  death  of  the  natural  industry. 
In  the  case  of  the  madder  plant,  the  natural 
source  of  the  dye  alizarin,  however,  this  has 
been  the  result.  A  visitor  to  the  South  of 
France,  surprised  at  the  absence  of  madder 
plantations  where  once  they  had  flourished, 
was  told,  when  he  asked  the  reason,  that 
"they  made  it  now  by  machinery."  In  the 
mineral  world  no  materials  are  known  of 
which  the  composition  has  not  been  ascer- 
tained, and  a  great  number  of  the  special 
crystallised  forms  of  minerals,  including  the 
gems,  ruby  and  diamond,  have  been  ^artifi- 
cially produced,  though  in  the  latter  case,  so 
far,  only  as  microscopic  crystals.  The  prog- 
ress of  synthesis,  or  the  building  up  of  natural 
materials  from  their  constituent  elements, 
proceeds  apace.  Even  some  of  the  simpler 
albuminoids,  a  class  of  substances  of  great 
importance  in  the  life  process,  have  recently 
been  artificially  prepared.  None  of  the 
known  materials  are  regarded  in  this  respect 
as  peculiar.  The  idea  that  a  peculiar  "vital 
force"  acted  in  the  chemistry  of  life  is 
extinct.  Some  of  the  natural  products  are 
known  to  be  exceedingly  complicated  in 
their  structure,  and  their  synthesis  is  there- 


46  MATTER  AND  ENERGY 

fore  proportionally  difficult.  But  progress 
is  steady.  The  modern  chemist  builds  up 
the  compounds  occurring  in  nature  from 
their  constituent  elements  as  an  architect 
causes  a  house  to  be  built  up  out  of  bricks 
and  mortar.  The  elements  are  the  bricks, 
and  energy  may  be  regarded  as  somewhat 
akin  to  the  mortar.  Naturally  occurring 
substances  form,  however,  only  one  class. 
Innumerable  entirely  new  compounds  have 
been  produced  in  the  last  century.  The 
artificial  dye-stuffs,  prepared  from  materials 
occurring  in  coal-tar,  make  the  natural 
colours  blush.  Saccharin,  which  is  hundreds 
of  times  sweeter  than  sugar,  is  a  purely 
artificial  substance.  New  explosives,  drugs, 
alloys,  photographic  substances,  essences, 
scents,  solvents,  and  detergents  are  being 
poured  out  in  a  continuous  stream.  The 
philosophic  blemish  that  there  are  still  eighty 
fundamental  forms  of  matter  instead  of  one, 
is  compensated  for  on  the  practical  and  utili- 
tarian side.  The  possible  new  combinations 
of  these  eighty  elements  among  themselves 
are  still  legion  in  spite  of  the  innumerable 
compounds  already  prepared.  What  wonder 
if  chemistry  amid  this  wealth  of  materials 
had  become  unphilosophical  and  had  almost 
ceased  to  ask  what  are  these  elements!  The 


MATTER:  I.  ATOMS  47 

very  idea  of  transmutation  was  gradually 
coming  to  be  looked  upon  as  a  lingering 
survival  of  an  ancient  heresy,  when,  quite 
unexpectedly,  it  was  demonstrated  that  the 
radioactive  elements  were  transmuting  them- 
selves. However,  these  developments  need 
not  be  considered  till  later.  The  best  intro- 
duction to  the  science  of  matter  is  got  by 
making  up  the  mind  frankly  to  accept  the 
separate  existence  of  almost  fourscore  dif- 
ferent elements,  each  something  of  a  law 
unto  itself,  having,  it  is  true,  most  marked 
and  important  analogies  with  the  others,  but 
not  directly  derivable  from  or  transformable 
into  any  of  them. 

Now,  if  we  follow  another  ancient  philo- 
sophical line  of  thought,  we  shall  arrive  at 
the  first  most  important  property  dis- 
tinguishing these  elements,  namely,  the 
relative  weights  of  their  atoms.  The  ancients 
asked  themselves  the  question  whether  matter 
occupied  space  continuously  or  discontinu- 
ously.  If  you  took  a  piece  of  solid  matter,  or 
a  drop  of  liquid,  and  divided  it  into  two 
equal  parts  and  then  subdivided  one  of  these 
parts  in  the  same  way  again  and  again,  can 
you  imagine  the  process  going  on  for  ever, 
or  would  you  at  last  arrive  at  the  "atom," 
as  they  called  it,  the  particle  so  small  that 


48  MATTER  AND  ENERGY 

it  could  not  be  further  divided?  Science  has 
definitely  adopted  the  view  of  the  "discrete" 
or  "grained"  structure  of  matter  as  opposed 
to  the  view  that  it  occupies  space  continu- 
ously. The  properties  of  gases  make  it  the 
only  possible  view  to  adopt.  Gases  differ 
from  liquids  and  solids  in  expanding  into 
and  uniformly  filling  every  empty  space  that 
offers  itself,  and  from  the  laws  they  obey  it  is 
possible  not  only  to  prove  definitely  that 
they  consist  of  small  particles  moving  about 
freely  in  space  with  great  velocity,  but  even 
to  count  the  number  of  particles  contained  hi 
any  quantity  of  a  gas.  These  particles  are 
not  called  "atoms,"  however,  but  "mole- 
cules." Let  us  suppose  that  we  had  chosen 
for  the  subdivision  process,  imagined  by  the 
Greeks,  a  drop  of  liquid  water — not,  that  is 
to  say,  one  of  the  fundamental  elementary 
substances,  but  a  compound  made  up  of  the 
two  elements,  hydrogen  and  oxygen.  On 
the  adopted  view,  at  some  stage  in  its  sub- 
division we  should  come  on  the  single  unit 
particle,  or  molecule,  of  water,  the  smallest 
particle  of  water  that  can  exist.  It  could 
not  properly  be  described  as  the  atom  of 
water,  because  although  it  represented  the 
limit  of  conceivable  mechanical  subdivision, 
it  can  still  be  decomposed,  like  any  other 


MATTER:  I.  ATOMS  49 

quantity  of  water,  into  its  constituent  ele- 
ments, hydrogen  and  oxygen,  by  chemical 
methods.  The  word  molecule  has  thus  been 
employed  to  represent  the  smallest  single 
particle  of  any  substance,  whether  elementary 
or  compound,  that  has  a  separate  existence; 
whilst  the  word  "atom"  has  been  used  to 
denote  a  constituent  elementary  particle  of  a 
molecule.  Thus  the  molecule  of  water  is 
known  to  consist  of  two  atoms  of  hydrogen 
and  one  of  oxygen.  The  conclusion  might  be 
jumped  at  that,  for  an  element,  the  molecule 
and  the  atom  are  the  same.  In  rare  cases 
they  are,  but  more  often  they  are  not.  The 
atoms  possess  certain  powers  of  combining 
with  other  atoms,  as  the  existence  of  com- 
pound substances  shows.  If  they  cannot 
get  other  atoms  to  unite  with  they  will  unite 
among  themselves.  Single  atoms  do  not,  as  a 
rule,  continue  to  exist  free  for  any  appreciable 
length  of  time.  At  the  moment  the  molecule 
is  broken  up  they  do  undoubtedly  start 
existence  single,  but  at  the  first  opportunity 
they  unite.  This  accounts  for  the  fact  that 
many  of  the  elements  at  the  moment  of 
their  formation,  or  in  the  "nascent  state"  as 
it  is  termed,  often  exhibit  extraordinary 
reactivity  and  bring  about  many  reactions 
which  the  same  elements  in  the  ordinary 


50  MATTER  AND  ENERGY 

state  are  quite  unable  to  effect.  The  mole- 
cules of  hydrogen,  oxygen,  and  nitrogen,  and 
most  of  the  elementary  gases,  consist  of  two 
atoms  of  these  elements.  But  another  gase- 
ous form  of  oxygen,  called  ozone,  is  known, 
the  molecule  of  which  consists  of  three 
atoms.  It  is  very  different  from  ordinary 
oxygen,  having  a  pungent  smell  and  being 
extremely  reactive,  so  that  it  instantly 
oxidises,  or  burns  up,  many  materials  not 
attacked  by  oxygen  at  ordinary  temperature. 
The  third  atom  is  in  the  proverbial  position 
of  not  being  wanted,  and  at  the  first  oppor- 
tunity takes  another  partner.  The  ozone 
molecule  separates  into  an  ordinary  oxygen 
molecule  and  a  single  free,  and  therefore 
exceedingly  active  oxygen  atom.  Then,  too, 
there  is  the  case  of  the  diamond.  Diamond 
is  the  purest  natural  form  of  the  element  car- 
bon, and  it  has  been  suggested  that  its  hard- 
ness, great  density,  etc.,  are  due  to  six  atoms 
of  carbon  being  combined  in  a  ring  to  form 
the  molecule, — a  form  of  union  which  is  a 
favourite  one  for  this  element  in  compounds. 
Ozone  and  diamond  are  both  converted  into 
the  commoner  varieties,  oxygen  and  carbon, 
by  the  simple  action  of  heat  alone,  which 
proves  their  identity  with  these  elements.  - 
The  rare  gases  of  the  atmosphere — helium, 


MATTER:  I.  ATOMS  51 

argon,  and  the  rest  of  the  family — are  unique 
in  possessing  no  power  of  combination. 
Hence  they  do  not  combine  with  themselves, 
and  their  molecules  are  composed  of  single 
atoms,  or,  -as  it  is  termed,  are  "monatomic." 
They  are,  speaking  anthropomorphically,  the 
misanthropes  among  matter.  Mercury  in 
the  form  of  vapour  is  the  only  known  similar 
case,  under  ordinary  circumstances,  though 
at  a  very  high  temperature  many  gaseous 
elementary  substances  are  more  or  less  com- 
pletely dissociated  into  single  atoms. 

Properties  which  furnished  the  basis  of  the 
Aristotelian  system  of  elements  depend  not 
only  on  the  constituent  materials,  but  on  the 
manner  in  which  their  atoms  are  arranged  in 
space  among  themselves.  When  compounds 
are  considered,  there  often  exist  several  en- 
tirely different  compounds,  having  the  same 
kind  and  same  number  of  atoms  in  their 
molecules,  differently  arranged.  These  are 
termed  "isomers." 

There  is,  however,  much  more  involved  in 
the  modern  terms  atom  and  molecule  than 
could  ever  be  derived  from  the  purely  de- 
ductive reasoning  of  ancient  philosophers. 
Indeed  these  conceptions  would  have  very 
little  scientific  value  if  it  were  not  for  one 
very  important  consideration  included  in  the 


52  MATTER  AND  ENERGY 

modern  use  of  the  terms.  If  any  one  kind  of 
elementary  or  compound  substance  is  con- 
sidered, the  atoms  or  molecules,  respectively, 
are  all  precisely  alike  down  to  the  minutest 
particular.  So  far  as  the  atoms  are  con- 
cerned this  holds  with  the  utmost  rigidity. 
As  regards  the  molecules,  there  are  certain 
substances,  called  "tautomeric,"  for  which 
it  is  believed  that  the  molecule  vibrates 
between  two  separate  configurations.  For 
these,  of  course,  the  statement  has  to  be 
suitably  qualified.  The  most  striking  evi- 
dence of  this  uniformity,  as  regards  atoms, 
is  furnished  by  the  sharpness  of  the  lines  of 
light  constituting  the  spectrum  of  the  element. 
These  lines,  as  will  be  shown,  must  originate 
from  the  vibrations  of  electrically  charged 
systems  associated  with  the  atoms;  and  if 
the  vibrations  of  different  atoms  were  in  the 
least  out  of  tune  with  one  another,  the  lines 
would  be  blurred  and  diffuse.  Professor 
Schuster  has  calculated,  from  the  sharpness 
of  the  spectrum  lines,  that  the  separate 
periods  of  vibrations  among  the  atoms  of  an 
element  do  not  differ  from  one  another  by 
so  muck  as  would  be  represented,  in  a  collec- 
tion of  clocks,  by  one  out  of  every  eight  losing 
or  gaming  a  second  in  every  twenty-three 
days.  But  chemistry  tells  the  same  story.  It 


MATTER:  I.  ATOMS  53 

draws  its  elementary  materials  from  widely 
different  localities  and  kinds  of  compounds. 
Yet  the  elements  show  no  differences  among 
themselves,  such  as  might  be  explained  by 
slight  differences  in  the  individual  atoms. 
Again,  the  spectroscope  tells  us  that,  in  the 
most  distant  stars,  the  same  elements  exist  as 
here,  and  that  the  periods  of  the  vibrations 
which  cause  them  to  emit  light  are  identical 
with  those  of  their  terrestrial  representatives. 
These  profound  conclusions  forced  them- 
selves first  on  chemists  in  their  study  of 
chemical  composition.  When  carbon  or 
charcoal  is  burnt  in  air  or  oxygen,  there  may 
be  two  different  kinds  of  compounds  pro- 
duced. If  there  is  plenty  of  oxygen,  the 
well-known  gas,  popularly  called  carbonic 
acid  gas,  and,  more  strictly,  carbon  dioxide, 
is  formed.  But  with  a  deficiency  of  air,  the 
highly  poisonous  and  entirely  different  gas, 
employed  in  lethal  chambers,  and  known  as 
carbon  monoxide,  results.  The  first  contains 
27.28%  carbon  by  weight  and  72.72%  of 
oxygen,  whilst  the  second  contains  42.86% 
of  carbon  and  57.14%  of  oxygen.  Quite  a 
large  number  of  commonly  occurring  com- 
pounds had  been  analysed  by  chemists  and 
the  composition  expressed  percentage-wise 
as  above,  before  it  occurred  to  Dalton,  the 


54  MATTER  AND  ENERGY 

founder  of  the  modern  Atomic  Theory,  to 
express  the  results  not  as  percentages,  but  in 
terms  of  a  unit  of  one  of  the  constituents. 
Thus  the  above  results  might  be  expressed  as 
the  amount  of  oxygen  combined  with  one 
gram,  ounce,  pound,  or  any  convenient  unit 
of  weight  of  carbon.  Then  it  is  seen  that, 
whilst  carbon  monoxide  contains  per  gram 
of  carbon  about  l£  grams  of  oxygen,  carbon 
dioxide  contains  about  2f  grams.  In  the 
first  case  the  amount  of  oxygen  is  exactly 
twice  t-hat  in  the  second.  This  "Law  of 
Multiple  Proportions"  was  found  to  extend 
to  all  compounds  in  which  the  same  elements 
united  in  different  proportions.  There  was 
only  one  conclusion  possible.  The  com- 
position by  weight  of  compounds  is  fixed 
and  definite.  Therefore  the  atoms,  or 
smallest  particles  which  combine  together, 
must  themselves  have  fixed  and  definite 
weight.  Moreover,  these  atoms  combine  as 
units.  One  atom  of  carbon,  as  in  the  present 
case,  may  combine  with  one  or  with  two 
atoms  of  oxygen,  but  not  with  one  atom  and  a 
fraction.  Henceforth  the  conception  of  the 
atom  became  more  than  a  mere  philosophical 
deduction.  It  is  a  necessity  to  explain  the 
experimental  facts  of  chemical  composition. 
It  would  take  us  too  far  out  of  our  course  to 


MATTER:  I.  ATOMS  55 

consider  at  any  length  in  what  way  this 
conception  has  grown  until  we  are  as  con- 
vinced of  the  existence  of  these  atoms  and  of 
their  uniformity  and  invariability  as  if  we 
could  count  and  measure  them.  Indeed, 
they  are  actually  counted  in  certain  special 
cases  in  radioactivity.  But  something  must 
be  said  as  to  the  manner  in  which  this  work 
has  culminated  in  assigning  to  each  element  a 
number  representing  the  relative  weight  of 
its  atom  in  terms  of  that  of  some  standard 
element. 

The  proportions  by  weight  of  the  elements 
in  compounds  give  us  the  relative  weights  of 
the  atoms  of  the  elements,  provided  always 
that  we  can  determine  the  relative  number 
of  atoms  of  each  element  in  the  molecule  of 
the  compound.  Thus,  in  the  compound 
carbon  monoxide,  the  oxygen  weighs  If  times 
as  much  as  the  carbon.  Before  we  can  con- 
clude that  the  single  atom  of  oxygen  weighs 
lj  times  that  of  the  single  atom  of  carbon, 
we  must  know  that  in  the  compound,  carbon 
monoxide,  there  are  equal  numbers  of  the 
two  kinds  of  atoms.  Dalton  guessed  this 
and  happened  to  be  correct,  but  many  of  his 
other  guesses  were  less  happy.  Really,  quite 
a  number  of  steps  are  involved  before  relative 
atomic  weights  can  be  deduced  from  the 


56  MATTER  AND  ENERGY 

chemical  composition.  The  first  step  is  to 
find  the  relative  weights  of  the  molecules  of 
as  many  of  the  compounds  of  the  element 
as  possible.  This  apparently  difficult  task 
is  in  reality  very  easily  accomplished,  because 
of  a  fundamental  generalisation  first  made 
in  the  beginning  of  the  last  century.  Equal 
volumes  of  all  gases  at  the  same  temperature 
and  pressure  contain  the  same  number  of 
molecules.  In  this  form  it  has  been  known 
successively  as  Avogadro's  rule,  Avogadro's 
hypothesis,  and,  lastly,  Avogadro's  law.  In 
the  first  instance  the  view  was  put  forward 
to  harmonise  Dalton's  theory  of  atoms  with 
some  very  simple  general  relations,  dis- 
covered by  Gay-Lussac,  between  the  volumes 
of  gases  which  combine  together  and  the 
volumes  of  the  products  resulting,  when 
these  also  are  gaseous.  If,  for  example, 
the  volumes  of  hydrogen  and  oxygen  are 
measured  which  combine  together,  when  the 
mixture  is  exploded  by  a  spark  or  a  flame, 
to  form  water,  and  all  the  measurements  are 
made  above  100°  C.,  so  that  the  water  pro- 
duced by  the  combination  remains  gaseous, 
as  steam,  it  is  found  that  the  volume  of 
hydrogen  is  almost  exactly  twice  that  of  the 
oxygen,  and  is  equal  to  that  of  the  steam 
resulting.  This  law  of  simple  combining 


MATTER:  I.  ATOMS  57 

volumes,  like  the  law  of  Multiple  Proportions, 
holds  for  all  combinations  between  gases. 
It  led  Avogadro  to  make  his  famous  sugges- 
tion. For,  on  his  view,  the  example  taken 
would  simply  mean  that  two  molecules  of 
hydrogen  unite  with  one  molecule  of  oxygen 
to  form  two  molecules  of  water.  If  the 
molecule  of  hydrogen  contains  the  same 
number  of  atoms  as  the  molecule  of  oxygen, 
this  means,  therefore,  that  one  atom  of  oxygen 
combines  with  two  atoms  of  hydrogen.  Since 
9  parts  by  weight  of  water  contain  1  part  of 
hydrogen  and  8  parts  of  oxygen  by  weight, 
the  atomic  weight  of  oxygen  in  terms  of  that 
of  hydrogen,  as  1,  is  approximately  16. 
Gradually  all  the  assumptions  have  been 
eliminated,  and  it  has  been  found  that  a 
variety  of  different  methods  confirm  the 
value  of  the  atomic  weights  obtained  in  this 
way.  Mainly  for  the  convenience  of  analysts 
the  unit  adopted  is  oxygen,  the  atomic 
weight  of  which  is  made  exactly  16.  On  this 
scale  that  of  hydrogen  is  1.008. 


58  MATTER  AND  ENERGY 

CHAPTER  IH 

MATTER:  11.  THE  ELEMENTS 

THE  special  science  of  matter,  or  chemistry, 
occupies  at  the  present  time  a  curious  inter- 
mediate position.  On  the  one  hand,  it  is 
connected  with  the  more  philosophical  science 
of  physics,  or,  to  use  an  older  term,  natural 
philosophy,  which  tirelessly  seeks  to  represent 
or  "explain"  natural  phenomena,  such  as 
light,  heat,  and  electricity,  with  the  minimum 
number  of  fundamental  assumptions,  and 
those  the  simplest  and  most  probable  it  is 
possible  to  conceive.  On  the  other  hand,  it 
is  connected  with  the  descriptive  sciences, 
embraced  under  the  old  term  natural  history, 
which  find  ready  to  hand  in  Nature  a  wealth 
of  forms  and  modifications,  connected  by 
more  or  less  close  analogies  and  relationships, 
divided  into  genera,  species,  and  varieties, 
and  in  which  the  power  of  artificially  repro- 
ducing the  work  of  Nature  is  either  very 
limited  or  does  not  exist.  Natural  philosophy 
may  "explain"  a  rainbow,  but  not  a  rabbit. 
A  rainbow  can  be  constructed  at  will  out  of 
perfectly  colourless  beginnings,  which  is  a 
proof  that  there  is  no  secret  about  a  rainbow 


MATTER:  II.  THE  ELEMENTS      59 

as  such.  But  nothing  but  rabbits  will  or 
can  produce  a  rabbit,  a  proof  again  that  we 
cannot  say  what  a  rabbit  is,  though  we  may 
have  a  perfect  knowledge  of  every  anatom- 
ical and  microscopic  detail.  Applying  the 
same  argument  to  matter,  we  may  have  a 
perfect  knowledge  of  every  reaction  and  prop- 
erty of  an  element,  may  know  the  wave 
length  of  every  line  in  its  spectrum  with  al- 
most incredible  accuracy,  may  have  studied 
every  possible  compound  of  it,  but  still  we  do 
not  know  what  a  single  element  really  is.  In 
this  sense  chemistry  is  a  purely  descriptive 
science.  Again  in  the  other  direction,  in  the 
chemistry  of  the  excessively  unstable  compli- 
cated compounds  which  constitute  the  living 
body,  the  science  is  again  descriptive,  although 
in  this  direction  every  year  the  philosophical 
domain  is  extended.  There  seems  no  limit  to 
possibilities  of  its  extension,  and  the  time  has 
gone  by  when  it  seemed  impious  even  to 
suggest  the  bare  possibility  of  our  one  day 
being  able  to  synthesise  food-stuffs  apart  from 
the  life  process.  Between  these  two  domains, 
and  within  these  limits,  the  science  of  matter 
is  as  philosophical  as  physics.  The  inquiring 
mind  is  more  or  less  satisfied  with  the  general 
explanation  of  the  countless  materials  which 
exist.  We  can  form  mental  pictures  of  their 


60  MATTER  AND  ENERGY 

inner  construction  and  can  put  them  together 
artificially,  in  many  cases  by  processes  more 
efficient  and  economical  than  the  natural 
ones.  Will  this  ever  be  true  of  the  elements 
themselves?  Between  the  completely  satis- 
fying explanation  of  things  and  the  mind  in 
ignorance  so  profound  that  it  does  not  know 
there  is  anything  possible  to  be  known,  is  a 
wide  region,  and  somewhere  in  this  gap  the 
science  of  the  elements  at  present  remains. 
There  are  two  possible  methods  of  advance. 
One  is  to  loose  the  reins  of  a  brilliant  imagina- 
tion, to  let  it  go  for  a  space  untrammelled 
by  the  limitations  of  knowledge,  and  only, 
at  the  end,  bring  the  consequences  of  the 
process  to  be  confirmed  or  rejected  by  fact. 
This  is  a  method  which,  traditionally,  has 
been  unduly  discouraged  by  chemists,  for  it 
is  rare  that  the  most  erroneous  theory,  if 
original,  and  capable  of  experimental  test, 
does  not  result  sooner  or  later  in  a  substan- 
tial increase  in  experimental  knowledge.  The 
other  method  is,  as  in  all  the  purely  descrip- 
tive sciences,  to  evolve  by  some  conprehen- 
sive  scheme  order  and  definiteness  out  of  the 
confused  fabric  of  resemblances  and  differ- 
ences, similarities  and  contrarieties,  among 
the  units  which  make  up  the  whole.  These 
eighty  or  more  elements,  each  of  which  is  a 


MATTER:  II.  THE  ELEMENTS      61 

fundamental  separate  existence,  exhibit 
among  themselves  the  most  remarkable  set 
of  resemblances  and  differences,  and  may  be 
divided  into  groups  or  families.  The  begin- 
ning of  a  comprehensive  scheme  expressing 
these  relationships  dates  from  the  middle  of 
last  century,  when  an  Englishman,  J.  A.  R. 
Newlands,  revealed  a  connection  between 
the  properties  of  the  chemical  elements  and 
the  weights  of  their  atoms  which  is  of  a  most 
curious  and  fascinating  kind.  He  seems  to 
have  been  a  man  of  little  force  of  character 
and  inexperience,  mistaking  scepticism  for 
criticism,  and  discouraged  thereby.  Scep- 
ticism is  always  with  us,  but  real  criticism  is 
the  rarest  thing  in  science;  for  criticism  in- 
volves knowledge  more  even  than  discovery. 
Newlands  was  a  pioneer,  and  mistakenly  in 
his  own  region  he  gave  to  authority  the 
deference  which  only  belongs  to  its  own.  In 
consequence,  his  idea  was  not  properly  de- 
veloped until  it  occurred  independently  to 
two  other  celebrated  chemists,  Mendelejeff 
and  Lothar  Meyer. 

If  the  elements  are  written  down  in  order 
of  their  atomic  weights,  beginning  with  the 
smallest,  the  successive  members  will,  as  a 
rule,  differ  abruptly  from  one  another  in 
general  character,  like  the  notes  in  a  scale  of 


62  MATTER  AND  ENERGY 

music;  but  after  a  certain  number  have  been 
set  down,  corresponding  with  the  number  of 
notes  in  an  octave,  the  general  character  of 
the  elements  already  set  down  will  be  repro- 
duced in  the  same  order  by  another  set.  It 
happened  that  in  Newlands'  time  the  number 
of  elements  that  had  to  be  passed  through 
before  the  initial  character  repeated  itself  was 
seven,  which  is  the  same  as  the  number  of 
notes  in  the  octave,  and  hence  he  called  the 
generalisation  the  Law  of  Octaves.  Owing 
to  the  discovery  of  the  new  family  of  similar 
elements  in  the  atmosphere,  beginning  with 
argon,  another  note,  so  to  speak,  has  to  be 
added  to  the  scale,  making  eight.  The 
Periodic  Classification,  in  one  of  the  various 
forms  in  which  it  is  now  usually  represented, 
is  shown  in  the  Table  (pp.  6-7).  The  ele- 
ments are  arranged  in  order  of  atomic  weight 
in  horizontal  columns  of  eight,  as  a  rule,  the 
elements  falling  under  each  other  in  vertical 
columns  being  analogous  to  each  other.  Each 
vertical  column  is  therefore  a  family  group 
and  is  indicated  by  the  number  0  to  7,  accord- 
ing to  its  position.  The  group  number  corre- 
sponds, as  a  rule,  with  the  valency  of  an  ele- 
ment, or  the  number  of  units  of  combining 
power  it  possesses.  The  zero  group  are  non- 
valent,  and  have  no  combining  power  what- 


MATTER:  II.  THE  ELEMENTS      63 

ever.  It  comprises  the  rare  gases  found  in  the 
atmosphere  whose  molecules  exist  as  single 
atoms  without  power  of  uniting  together. 
Group  I  contains  the  monovalent  metals  of 
the  alkalies;  these  unite  with  one  other  monov- 
alent atom,  such  as  chlorine.  Thus  common 
salt  is  a  compound  of  one  atom  of  sodium 
and  one  of  chlorine.  Group  II  contains 
the  divalent  metals  of  the  alkaline-earth 
family,  of  which  calcium  is  the  commonest. 
Common  lime  is  a  compound  of  one  atom  of 
calcium  and  one  of  the  divalent  element  oxy- 
gen. Group  III  contains  the  trivalent  earth 
elements,  of  which  alumina,  the  oxide  of  alu- 
minium, a  compound  containing  two  atoms 
of  aluminium  and  three  of  oxygen,  is  typical. 
The  next  group  are  tetravalent,  and  contain 
some  of  the  most  important  elements,  like 
carbon  and  silicon,  the  oxides  of  which  have 
two  atoms  of  oxygen  to  one  of  the  element. 
After  this  the  elements  usually  act  with 
several  valencies  forming  different  classes 
of  compounds,  and  the  group  number  rep- 
resents the  maximum  valency.  The  most 
common  valency  is  8  minus  the  group  number, 
so  that  Group  V  is  generally  trivalent, 
Group  VI  divalent  and  Group  VII  mo- 
novalent again.  Groups  I  to  III  comprise 
the  metals  which,  combined  with  oxygen, 


64  MATTER  AND  ENERGY 

form  alkalies  or  bases.  The  last  three  groups 
contain  the  non-metals  which,  when  united 
with  oxygen,  form  the  acidic  oxides.  Group 
V  contains  nitrogen  and  phosphorus,  which 
with  carbon,  hydrogen,  and  oxygen  play  the 
largest  part  in  the  constitution  of  living 
matter.  Group  VI  contains  the  sulphur 
elements  in  addition  to  oxygen,  and  Group 
VII  the  halogen  elements,  fluorine,  chlorine, 
bromine,  and  iodine.  In  general  it  may  be 
said  that  the  greater  the  difference  between 
the  group  numbers  of  two  elements,  the 
greater  the  probability  that  they  will  combine 
together  energetically  and  form  well-defined 
compounds  not  easy  to  decompose  again. 
In  the  Table,  the  symbol  of  the  element  and 
the  value  of  its  atomic  weight  are  placed 
below  it.  A  line  in  a  blank  space  indicates 
that  probably  a  still  undiscovered  element 
exists  there. 

The  Periodic  Classification  is,  however, 
by  no  means  so  simple  or  perfect  as  has  been 
indicated.  The  simple  period,  or  "octave" 
of  eight  elements,  applies  strictly  only  to  the 
first  sixteen  elements,  which  are  in  many  ways 
rather  different  from  the  subsequent  heavier 
elements.  To  understand  the  Periodic  Clas- 
sification fully  would  require  an  intimate 
detailed  knowledge  of  the  individual  character 


MATTER:  II.  THE  ELEMENTS      65 

of  each  of  the  known  elements.  The  more 
highly  trained  a  chemist  is  in  this  direction 
the  more  will  he  see  to  interest  and  attract 
his  attention  in  the  Periodic  system.  Its 
apparent  defects  as  well  as  its  obvious  advan- 
tages will  give  food  for  thought  probably 
for  a  long  time  to  come.  Strictly  speaking, 
it  has  no  defects;  for  it  is  no  theory,  but  a 
simple  mode  of  expressing  the  facts.  Like 
the  elements  it  represents,  it  is  a  law  unto 
itself.  It  cannot  be  explained,  but  only 
described  and  pondered  over.  There  are 
at  least  two  flat  contradictions  to  the  general 
order  of  the  atomic  weights.  Argon  has  an 
atomic  weight  slightly  greater  than  that  of 
potassium,  and  cannot  do  other  than  precede 
it.  Whilst  iodine  has  an  atomic  weight 
lower  than  tellurium,  and  cannot  precede  it 
in  the  classification  without  entirely  break- 
ing up  similar  families.  These  "exceptions" 
must  be  accepted  as  part  of  the  scheme.  In 
spite  of  all  the  determinations  they  have 
stimulated  of  the  atomic  weights  of  the  ele- 
ments in  question,  the  anomalies  have  only 
been  confirmed.  After  the  first  two  periods, 
each  of  eight  elements,  the  third  begins  and 
runs  half  through  as  far  as  Group  IV  before 
any  difference  becomes  apparent.  Then 
follow  no  less  than  ten  members  (vanadium 


66  MATTER  AND  ENERGY 

to  germanium)  enclosed  in  the  Table  between 
brackets,  which  are,  so  to  speak,  interpolated 
suddenly  into  the  period,  before  the  char- 
acteristics we  have  been  led  to  expect  from 
the  previous  members  of  Groups  V,  VI,  and 
VII  fully  reappear.  The  next  period  is  a 
repetition  of  the  last.  There  are  five  normal 
representatives  of  Groups  0  to  IV,  then 
nine  "interpolated"  elements  (one  is  still 
unknown)  exactly  analogous  to  the  preced- 
ing set  of  ten,  before  the  elements  of  Groups 
V  to  VII  are  again  met  with.  The  next 
period  begins  normally  with  three  perfect 
representatives  of  Groups  0  to  II,  and  then 
a  startling  change  takes  place.  When  Group 
III,  the  group  of  the  "earth  elements," 
is  reached,  we  begin  the  special  family 
of  elements  known  as  the  Rare-Earth  Ele- 
ments, of  which  no  less  than  thirteen  are 
known,  with  atomic  weights  fairly  distributed 
between  139  and  174.  They  resemble  one 
another  with  such  extraordinary  closeness, 
that  the  task  of  their  separation  and  purifica- 
tion from  one  another  is  one  of  the  most 
laborious  and  lengthy  operations  the  chemist 
is  acquainted  with.  For  this  reason  it  is 
difficult,  even  with  the  aid  of  the  spectro- 
scope, to  say  exactly  how  many  exist.  The 
members  of  this  set  of  elements  are  all,  like 


MATTER:  II.  THE  ELEMENTS      67 

the  earth-elements,  trivalent.  In  them  the 
simple  principle  of  the  Periodic  Law,  that 
each  increase  in  atomic  weight  causes  a  step 
by  step  change  in  chemical  character  and 
valency,  as  illustrated  by  the  passage  from 
group  to  group,  utterly  breaks  down.  In 
spite  of  their  name  they  now  result  in  large 
quantities  as  a  by-product  of  the  thorium 
industry.  With  the  exception  of  cerium,  a 
minute  proportion  of  which  is  used  with 
thorium  in  the  incandescent  gas  mantle, 
they  are  at  present  all  technically  worthless 
elements.  Advancing  in  atomic  weight  be- 
yond these  elements  we  emerge  at  the 
beginning  of  a  batch  of  nine  new  "inter- 
polated" elements,  perfectly  repeating  the 
characteristics  of  the  last  batch  of  nine,  the 
same  member  being  missing  in  each.  After 
them  only  one  representative  of  Groups  V  to 
VII  (bismuth,  Group  V)  is  known,  and  in 
the  next  period  the  sole  representatives  are 
radium  (Group  II)  and  thorium  (Group  IV). 
The  last  element  of  all  is  uranium.  These 
three  elements,  which  end  the  Table,  are  the 
ones  with  the  heaviest  atoms  known,  and  are 
all  unstable,  breaking  up  spontaneously  and 
exhibiting  in  the  process  the  recently  dis- 
covered property  of  radioactivity. 

What  have  been  termed  for  purposes  of 


(58  MATTER  AND  ENERGY 

identification  "  interpolation  elements  "  are 
all,  without  exception,  well-defined  metals. 
There  are  thirty  places,  and  twenty-eight  of 
them  are  known.  They  comprise  some  of 
the  technically  most  valuable  metals,  includ- 
ing the  iron  group,  and  the  whole  of  the  "  noble 
metals"  used  in  the  making  of  jewellery. 
They  differ  among  themselves  less  markedly 
and  distinctly  in  passing  from  member  to 
member  than  in  the  other  portions  of  the 
Periodic  Table.  At  the  same  time  the  whole 
truth  is  by  no  means  expressed  by  taking 
them  entirely  out  of  the  Table  and  putting 
them  in  a  part  by  themselves.  The  first 
three  members  have  obviously  resemblances 
of  a  most  interesting  kind  with  the  Groups  V 
to  VII  elements  where  they  would  naturally 
fall,  and  the  last  four  with  the  Groups  I  to  IV 
elements,  especially  in  that  their  usual 
valency  is  the  same  as  corresponds  with  these 
groups.  For  this  reason  it  is  usual  only  to 
take  out  the  three  middle  members,  the  iron 
group  and  the  light  and  heavy  platinum 
metals,  and  to  put  these  into  the  so-called 
Group  VTII,  as  shown  in  the  Table. 

Nearly  all  the  physical  properties  of  the 
elements,  their  density,  melting  point,  boiling 
points,  etc.,  are,  like  the  chemical  nature, 
periodic  properties  —  that  is  to  say,  they  vary 


MATTER:  II.  THE  ELEMENTS      69 

with  the  atomic  weight  periodically.  Especi- 
ally is  this  true  for  the  density.  Instead  of 
density,  or  weight  of  unit  volume,  the  relation 
is  most  clearly  expressed  by  plotting  against 
the  atomic  weight  the  atomic  volume,  which 
is  the  atomic  weight  divided  by  the  density, 
and  expresses  the  relative  volume  occupied 
by  the  individual  atoms.  The  elements  of 
Groups  I  to  IV  all  occupy  the  maxima  of  the 
curve  and  the  immediately  following  steeply 
descending  portions.  In  this  region  increase 
of  atomic  weight  is  followed  by  decrease  in 
the  space  occupied  by  the  atom.  The  oxides 
of  these  elements  show  strong  basic  or  al- 
kaline character,  uniting  eagerly  with  acids. 
On  the  other  hand,  the  characteristics  of 
Groups  V  to  VII  are  the  opposite.  Here  the 
elements  are  on  steeply  ascending  portions 
of  the  curve,  increase  of  atomic  weight  caus- 
ing great  increase  in  the  space  occupied  by 
the  atom.  The  oxides  of  these  elements 
are  strong  acids.  What  have  been  termed 
the  "interpolated"  elements  occupy  the 
minima  between  the  peaks  or  maxima,  and 
the  atomic  volume,  like  the  other  properties, 
does  not  show  any  great  change  in  passing 
from  one  member  to  the  next.  The  infusible 
and  non-volatile  elements  occupy  the  minima 
of  the  curves  throughout  and  in  enumerating 


70  MATTER  AND  ENERGY 

the  elements  which  have  been  successfully 
employed  in  the  manufacture  of  filaments 
for  electric  lamps,  where  these  two  qualities 
are  essential,  platinum,  carbon,  tungsten, 
tantalum,  osmium  (osram  is  a  trade  name 
for  tungsten),  it  will  be  found  that  these 
elements  all  occupy  low  positions  on  the 
curve.  Some  of  these  elements,  for  example, 
tantalum,  had  never  been  prepared  in  the 
pure  state  prior  to  their  technical  production 
as  lamp  filaments. 

The  difficult  task  of  evolving  order  and 
system  out  of  the  properties  of  the  large 
number  of  distinct  chemical  elements,  with 
their  infinitely  variegated  natures,  has  thus 
been  more  or  less  satisfactorily  accomplished. 
The  Periodic  Classification  which  connects 
all  the  properties  with  the  one  constant,  the 
relative  weight  of  the  atom  of  the  element, 
has  proved  a  veritable  mariner's  chart  and 
compass  to  the  investigator.  To  the  philos- 
opher, however,  it  is  a  completely  unsolved 
riddle,  the  meaning  of  which  seems  scarcely 
hidden  beneath  the  surface  and  yet  perpet- 
ually eludes  the  grasp.  These  numbers, 
expressing  the  relative  weights  of  the  atoms, 
are  so  many  cryptic  symbols  which  un- 
doubtedly have  a  profound  meaning,  but 
which  nevertheless  remain  mere  numbers. 


HEAT  AND  THEORY  OF  MATTER  71 

Hundreds  of  patient  investigators  have  de- 
voted years  of  strenuous  labour,  not  a  few 
their  whole  working  lives,  to  the  task  of 
determining  these  natural  constants  with  the 
greatest  possible  accuracy,  and  the  work 
still  progresses  steadily.  Some  are  known 
with  a  degree  of  precision  unsurpassed  any- 
where in  the  exact  sciences,  and  scarcely  any 
are  likely  to  be  very  seriously  in  error.  The 
second  or  speculative  method  of  attacking 
the  problem  of  the  nature  of  the  elements 
has  scarcely  advanced  far  enough  to  deserve 
detailed  consideration  in  a  book  of  this 
character. 


CHAPTER  IV 

HEAT  AND   THE   KINETIC   THEORY  OP  MATTES 

SCIENCE  is  not  an  affair  of  watertight 
compartments.  We  cannot  accept  the  idea 
of  molecules  and  atoms  in  explanation  of 
the  properties  of  matter  and  deny  their 
existence  when  we  approach  the  study  of 
heat.  Like  twin  dewdrops  forming  side  by 
side,  these  two  great  divisions  of  science  have 
at  length  met  and  coalesced.  The  conception 


78  MATTER  AND  ENERGY 

of  the  atomic  and  molecular  structure  of 
matter  carries  with  it  the  complete  and 
satisfying  explanation  of  the  kind  of  energy 
classed  as  heat. 

Energy  may  sleep  indefinitely  in  matter,  in 
one  of  its  numerous  potential  forms,  without 
any  indication  of  its  presence.  It  is  only 
perceptible  when  in  the  kinetic  form  as 
mechanical  energy  or  the  kinetic  energy  of 
moving  masses,  as  electrical  energy  or  the 
kinetic  energy  of  moving  electrons,  and  so  on. 
Now  in  the  real  world  as  contrasted  with  the 
ideal  world  of  the  mathematical  physicist,  a 
convenient  mental  creation  of  frictionless 
machines,  weightless  moving  parts,  thermally 
impervious  partitions,  etc.,  energy  when  in 
the  kinetic  form  invariably  passes  naturally 
into  heat  energy.  If  the  kinetic  energy  is 
uncontrolled,  the  whole  of  it  rapidly  assumes 
the  form  of  heat.  By  the  use  of  properly 
constructed  machines  some  part  of  it  may  be 
converted  into  other  forms;  for  example,  the 
kinetic  energy  of  the  electric  current  passing 
through  an  electric  motor  may  give  rise  to  a 
certain  proportion  of  the  total  energy  in  the 
form  of  mechanical  energy.  In  this  case 
only  a  small  part,  represented  by  frictional 
and  resistance  losses,  goes  directly  into  heat. 
But  in  due  course  the  whole  of  the  energy 


HEAT  AND  THEORY  OF  MATTER  73 

sooner  or  later,  and  usually  sooner  rather  than 
later,  is  quantitatively  converted  into  heat. 
In  the  potential  form,  in  coal,  it  has  persisted 
for  untold  ages.  Once  released,  heat  is  the 
sole  ultimate  product.  By  the  law  of  con- 
servation none  is  lost  in  the  process,  and  the 
total  amount  of  heat  obtained  is  precisely 
the  same,  whether  it  raises  steam  in  boilers, 
is  converted  into  mechanical  power  by  an 
engine,  then  into  electrical  power  by  a  dy- 
namo, is  transmitted  by  conductors  as  electric 
current  to  a  far  distant  place,  there  to  be 
reconverted  into  mechanical  power  and  back 
into  heat  again  by  friction.  Heat  energy 
may  or  may  not  be  convertible  into  other 
forms,  according  to  its  temperature  and  the 
temperature  of  the  surroundings.  In  the 
real  world  all  substances  conduct  heat, 
and  by  this  process  all  temperature  differences 
are  equalised  naturally.  The  whole  earth, 
with  slight  differences  in  different  places 
maintained  by  meteorological  causes,  acts  as 
the  reservoir  or  sink  of  heat  at  uniform 
temperature,  into  which  all  the  energy 
liberated  in  the  world  and  assuming  the 
kinetic  form,  flows  without  perceptibly  affect- 
ing its  temperature. 

Heat  when  it  has  assumed  the  common 
level  of  temperature  by   natural   agencies, 


74  MATTER  AND  ENERGY 

such  as  conduction,  is  still  energy  in  the 
kinetic  form.  Why  does  the  process  of  trans- 
formation stop  there?  If  energy  is  the 
universal  commodity  on  which  all  life  depends 
and  all  civilisation  feeds,  why  has  it  not  been 
found  possible  to  draw  on  the  immense 
reservoir  of  heat  energy  in  the  earth,  the 
ocean,  or  the  air,  and  to  convert  it  back  again, 
so  solving,  once  for  all,  the  dream  of  perpetual 
motion?  Such  a  perpetual  motion  machine 
would  not  contradict  the  first  law  of  energy, 
the  law  of  conservation,  but  it  would  the 
second  law,  the  law  of  availability.  This 
law,  realised  as  soon  as  the  doctrine  of  energy 
and  its  transformation  was  developed,  is,  in 
origin,  an  arbitrary  law,  no  reason  being 
assigned.  Like  the  Periodic  System,  it  was 
part  of  a  descriptive  science,  a  statement  of 
the  facts  found  by  experiment.  Its  philo- 
sophical foundations  remained  till  recently 
as  obscure  as  those  of  the  Periodic  Law. 

Imagine  a  machine,  installed,  for  example, 
on  an  Atlantic  liner,  capable  of  drawing  upon 
the  infinite  supply  of  heat  energy  of  uniform 
temperature  in  the  ocean,  cooling  the  ocean 
inappreciably  and  converting  the  heat  into 
the  mechanical  work  employed  in  propelling 
the  vessel,  the  heat  being  returned  to  the 
ocean  again  by  the  process  of  friction  between 


HEAT  AND  THEORY  OF  MATTER  75 

the  vessel  and  the  water.  The  second  law 
states  baldly  that  such  a  machine  is  im- 
possible even  to  conceive,  without  any 
reference  to  impossibility  of  construction. 
This  argument  has  been  frequently  used  in 
thermo-dynamics,  and,  in  spite  of  its  appar- 
ently negative  character,  no  theorem  has 
been  more  fruitful  in  leading  to  positive  dis- 
coveries. The  favourite  method  was  first  to 
try  to  conceive  such  a  machine.  One  of  the 
earliest  examples  made  use  of  the  freezing 
of  water.  Water,  unlike  most  other  liquids, 
expands  considerably  in  volume  when  it 
turns  into  ice,  and,  as  is  well  known  from  the 
bursting  of  even  strong  steel  vessels  by  the 
freezing  of  water,  is  capable  of  exerting  con- 
siderable pressure,  which,  just  as  in  the  case 
of  steam,  can  be  conceived  to  be  used  to  drive 
an  engine.  James  Thomson  found  that  a 
perpetual  motion  machine  of  the  kind  de- 
scribed could  be  imagined,  fulfilling  the 
scientific  conditions  rigidly,  provided  that  the 
freezing  point  of  water  did  not  change  when 
the  pressure  was  increased.  As  befitted  one 
of  those  associated  with  the  development  of 
the  laws  of  energy,  he  did  not  imagine  that  he 
had  found  a  case  which  upsets  the  second  law, 
but  he  argued  that  the  freezing  point  must 
change  with  increase  of  pressure,  and,  more- 


76  MATTER  AND  ENERGY 

over,  must  become  the  lower  the  higher  the 
pressure.  Experiment  proved  that  he  was 
right.  Ice  melts  under  great  pressure  without 
rise  of  temperature,  and  freezes  again  when 
the  pressure  is  relieved.  Most  other  liquids 
which  contract  when  they  become  solid  have 
their  solidification  points  increased  by  in- 
crease of  pressure.  Thus,  by  the  use  of  the 
doctrine  of  the  Impossibility  of  Perpetual 
Motion,  there  was  predicted  a  quite  unknown 
connection  between  the  change  of  volume 
experienced  by  a  liquid  freezing  on  the  one 
hand,  and,  on  the  other,  the  influence  which 
increase  of  pressure  has  on  its  freezing  point. 
This  paved  the  way  for  a  host  of  valuable 
predictions  of  a  similar  kind,  connecting  a 
variety  of  the  physical  properties  of  sub- 
stances together,  which  by  no  simple  process 
of  reasoning  could  be  shown  to  be  at  all 
connected.  In  no  single  case  have  these  in- 
numerable predictions  been  falsified  by  experi- 
ments, and  they  therefore  afford  a  purely 
experimental  proof  of  the  doctrine  denying 
the  possibility  of  perpetual  motion  and  of 
utilising  the  waste  heat  energy  of  uniform 
temperature. 

To  understand  more  clearly  the  reason  why 
perpetual  motion  is  impossible  in  the  sense 
laid  down,  we  have  merely  to  open  our  eyes 


HEAT  AND  THEORY  OF  MATTER  77 

to  see  things  as  they  are,  and  not  as  they 
appear  to  be  to  our  grossly  insensitive 
unaided  sight.  All  matter  is  composed  of 
molecules,  or  units  of  division  of  definite 
mass,  and  these  almost  infinitely  small 
molecules  do  not  occupy  space  continuously. 
Even  if  we  could  see  these  molecules  indi- 
vidually we  should  not  probably  know  any 
more  about  them  in  consequence  than  we 
do  already;  for  of  late  years  we  have,  thanks 
to  radioactive  phenomena,  been  able  to 
apprehend  them  as  individuals,  and  even  to 
count  their  numbers  with  results  in  startling 
agreement  with  previous  deductions.  But 
if  we  could  see  matter  as  it  is,  instead  of 
the  gross  masses  which  alone  appeal  to  our 
senses,  we  should  exclaim,  "Perpetual  motion 
impossible?  Why,  there  is  nothing  else  in 
the  whole  universe!"  To  do  so  we  need 
not  even  imagine  the  impossible.  All  that 
is  necessary  is  to  look  through  a  good  micro- 
scope with  a  high  power  lens  at  some  turbid 
liquid,  that  is,  some  liquid  containing  a 
cloud  of  very  small  solid  suspended  particles, 
just  visible  under  the  high  magnification 
employed.  We  shall  see  not  a  single  one  of 
these  particles  at  rest.  Each  is  animated 
with  the  most  lively  and  independent  move- 
ment, darting  hither  and  thither,  turning 


78  MATTER  AND  ENERGY 

and  reversing  all  the  time,  so  that  the  whole 
scene  is  a  veritable  dance  of  particles  in 
and  out  of  the  field  of  vision.  Hour  after 
hour  and  year  after  year  the  dance  goes  on 
undiminished,  independent  of  time  and  place 
and  of  the  nature  of  the  particles,  except 
that  the  smaller  they  are  the  more  lively 
is  their  movement.  It  is  the  Brownian 
movement,  discovered  in  1827  by  the  famous 
botanist  Robert  Brown;  and  this  state  of 
commotion,  which  is  the  normal  condition  of 
objects  still  large  enough  to  be  perceived, 
gives  a  faint  indication  of  the  normal  con- 
dition of  the  almost  infinitely  smaller  world 
of  molecules. 

Matter  exists  in  three  states,  the  gaseous, 
liquid,  and  solid.  The  condition  of  things 
obtaining  in  the  first  two  of  these  states  is 
very  completely  known,  whilst  of  the  third 
little  that  is  quite  definite  can  yet  be  said. 
The  gaseous  state  is  distinguished  by  the 
property  of  the  matter,  unless  it  is  com- 
pletely retained  by  a  closed  vessel,  of  diffus- 
ing out  and  filling  all  the  available  space 
offered  to  it  uniformly.  It  is  of  no  conse- 
quence whether  the  space  in  question  is 
entirely  empty  or  vacuous,  or  whether  it 
is  already  occupied  by  another  gas.  Each 
gas  by  diffusion  fills  the  whole  space  uni- 


HEAT  AND  THEORY  OF  MATTER  79 

formly  as  though  the  other  was  not  present, 
so  that  after  a  time  the  composition  through- 
out is  uniform,  whatever  it  was  to  start 
with.  From  this  we  may  argue  that  when 
uniformity  has  been  attained  the  process  of 
mixing  by  no  means  ceases,  though  no 
further  change  of  concentration  in  the  differ- 
ent parts  can  occur.  If  a  closed  bottle 
of  a  gas  with  powerful  odour  is  opened  in 
one  corner,  rapidly  the  gas  makes  its  presence 
known  throughout  the  whole  room;  whilst 
if  the  bottle  contained  air  only  it  would 
make  its  way  throughout  the  room  no  less 
quickly,  though  no  evidence  of  the  fact 
might  be  apparent.  The  older  school  tried 
hard  to  account  for  these  properties  by 
assuming  that  the  particles  of  gases  repel 
one  another.  The  present  school  found  a 
more  solid  foundation  to  build  upon  when 
they  regarded  the  molecules  of  a  gas  as  in 
perpetual  motion.  So  far  from  repelling  one 
another,  molecules  in  most  cases  tend  to 
move  together.  When  the  kinetic  energy 
of  the  moving  molecules  is  reduced  so  much 
by  lowering  the  temperature  that  this  ten- 
dency can  produce  its  effect,  the  gas  con- 
denses to  a  liquid. 

The  kinetic  theory  of  gases,  as  it  is  called, 
imagines  all  the  individual  molecules  of  a 


80  MATTER  AND  ENERGY 

gas  to  be  moving  about  with  very  great 
velocities  quite  independently  of  one  another, 
but  incessantly  colliding  together  with  them- 
selves and  with  the  walls  of  the  containing 
vessel,  rebounding  and  incessantly  repeating 
the  process.  These  impacts  on  the  walls 
generate  the  pressure  that  the  gas  exerts  out- 
wards, and  if  the  walls  were  not  there  noth- 
ing, except  the  mutual  encounters  between 
the  molecules,  would  hinder  the  free  pass- 
age of  the  gas  outward  into  space.  The  higher 
the  temperature  the  greater  the  pressure 
exerted  by  any  given  quantity  of  gas  confined 
in  any  space  of  given  volume,  and  this 
increase  of  pressure  with  temperature  is 
very  nearly  the  same  for  all  gases.  Now, 
since  the  mass  of  the  gas  is  not  changed  by 
the  rise  of  temperature  whilst  the  pressure 
is,  rise  of  temperature  must  make  the  impacts 
on  the  walls  either  more  numerous  or  more 
violent,  or,  in  general,  both  more  numerous 
and  more  violent.  Hence  it  was  deduced 
that  equal  rise  of  temperature  increases  the 
kinetic  energy  of  all  gases,  regardless  of  the 
nature  or  mass  of  their  molecules,  to  the 
same  proportionate  extent. 

The  problems  that  presented  themselves 
to  the  mathematician  in  this  theory  did  not 
prove  as  formidable  as  might  have  been 


HEAT  AND  THEORY  OF  MATTER  81 

expected.  They  asked  themselves  Avoga- 
dro's  question.  Consider  two  different  gases, 
for  example,  hydrogen  and  oxygen.  Let 
equal  volumes  of  each  gas,  measured  at  the 
same  pressure  and  the  same  temperature, 
be  compared.  What  are  the  relative  num- 
bers of  molecules  in  each?  Avogadro,  it  will 
be  recalled,  had  answered  this  question 
simply  by  intuition,  and  had  stated  that  the 
number  of  molecules  in  equal  volumes  of  all 
gases  measured  under  the  same  conditions 
is  the  same,  and  thus  had  laid  down  the 
fundamental  generalisation  which  had  en- 
abled chemists  to  determine  relative  atomic 
weights  and  to  discover  the  Periodic  Law. 
The  mathematicians  approached  the  sub- 
ject from  the  view  that  since  the  gases  are 
(1)  at  the  same  pressure,  the  kinetic  energy 
of  the  molecules  taken  as  a  whole  in  each  set 
must  be  the  same,  and  (2)  at  the  same  tem- 
perature, the  kinetic  energies  of  each  set  of 
molecules  will  remain  the  same  as  they  were 
before,  after  they  are  mixed.  In  investigat- 
ing the  general  conditions  for  two  sets  of 
independently  moving  molecules  to  be  able 
to  intermingle  without  any  transference  of 
energy  from  one  set  to  the  other,  they  de- 
duced that,  on  the  average,  the  kinetic  energy 
of  the  individual  molecules  in  the  two  sets 


82  MATTER  AND  ENERGY 

must  also  be  equal.  But  the  total  kinetic 
energy  is  the  same  for  both  gases.  Therefore 
the  numbers  of  their  molecules  must  be  equal. 
Avogadro's  rule  became  merely  one  conse- 
quence of  a  great  general  dynamical  theorem 
which  applies  to  any  system,  whether  a  gas 
or  not,  which  consists  of  a  vast  swarm  of 
free  unhampered  and  independently  moving 
small  units  of  mass,  incessantly  colliding 
with  each  other  and  rebounding.  The  the- 
orem is  known  as  the  law  of  equipartition 
of  energy.  The  molecule  of  hydrogen,  on 
the  average,  has  the  same  kinetic  energy  as 
the  molecule  of  oxygen  at  the  same  tem- 
perature. Since  the  kinetic  energy  is  pro- 
portional to  the  product  of  the  mass  into 
the  square  of  the  velocity,  and  the  molecule 
of  oxygen  is  sixteen  times  as  heavy  as  that 
of  hydrogen,  the  mean  velocity  of  the  hydro- 
gen molecule  must  be  four  times  that  of  the 
oxygen  molecule,  and  so  on  for  all  other 
molecules.  Gradually  all  uncertainty  has 
been  eliminated  from  this  conception;  and, 
as  already  remarked,  it  would  add  little, 
probably,  to  our  knowledge  if  we  could 
weigh,  count,  and  measure  the  velocity  of 
these  molecules  of  gases  individually.  Every 
cubic  centimetre  of  any  gas,  measured  under 
standard  conditions  (0°  C.  and  760  milli- 


HEAT  AND  THEORY  OF  MATTER  83 

metres,  barometric  pressure)  contains  twenty- 
seven  million  million  million  molecules.  The 
weight  of  the  single  molecule  of  hydrogen  is 
about  three  million-million-million-millionths 
of  a  gram,  and  its  velocity  at  0°  C.  is  rather 
more  than  a  mile  a  second.  The  hydrogen 
molecule  is,  it  is  true,  the  smallest  and  simplest 
molecule  of  matter  known,  but  it  is  a  large 
and  sluggishly  moving  individual  compared 
with  another  known  particle,  the  electron 
or  atom  of  negative  electricity.  The  average 
kinetic  energy  of  all  molecules  is  increased 
to  the  same  extent  by  rise  of  temperature, 
as  also  is  necessary  from  the  law  of  equi- 
partition  of  energy,  which  does  not  hold 
merely  for  one  particular  temperature,  but 
for  all  temperatures. 

Now  what,  exactly,  is  meant  by  tempera- 
ture? The  various  thermometric  scales  of 
Fahrenheit,  Centigrade,  and  Reaumur  came 
into  use  before  the  nature  of  heat  was  fully 
understood,  and  all  started  from  the  prop- 
erties of  the  substance  water.  Thus  the 
Centigrade  scale,  adopted  in  science,  calls 
the  freezing  point  of  water  zero,  or  0°  C.,  and 
the  boiling  point  of  water  under  normal 
barometric  pressure  100°  C.,  the  interval 
between  being  divided  equally  into  100 
parts  or  degrees  Centigrade.  Temperatures 


84  MATTER  AND  ENERGY 

below  zero  Centigrade  are  represented  by 
the  negative  sign.  Now  it  is  quite  obvious 
that  if  heat  energy  is  the  kinetic  energy  of 
moving  molecules,  although  there  is  no 
necessary  upper  limit  to  the  extent  a  substance 
may  be  heated  and  to  the  temperature  it 
may  acquire,  there  is  a  very  definite  limit  to 
the  extent  that  it  can  be  cooled.  A  sub- 
stance composed  of  molecules  at  rest  is 
absolutely  cold,  and  no  substance  can  be 
imagined  to  be  colder.  The  absolute  zero 
of  temperature  is  the  true  zero  of  a  thermo- 
metric  scale,  not  the  freezing  point  of  water 
or  of  any  other  substance. 

Few  people  who  have  not  thought  deeply 
in  the  subject  realise  what  a  confused  medley 
of  vague  and  disconnected  ideas  are  concealed 
within  the  common  uses  of  the  word  Tempera- 
ture. In  truth,  the  term,  even  in  science, 
has  changed  its  significance  almost  with 
every  decade  of  the  last  century.  It  is  more 
convenient  to  defer  the  discussion  of  what 
we  really  mean  by  the  word  "Temperature" 
until  the  next  chapter.  It  may  merely  be 
remarked  in  passing  that  the  term  in  its 
philosophical  sense  has  a  far  more  funda- 
mental meaning  than  that  used  in  the  science 
of  practical  thermometry,  which  refers  tem- 
peratures to  the  instruments  and  scales 


HEAT  AND  THEORY  OF  MATTER  85 

in  current  use,  just  as  weights  and  measures 
are  referred  to  the  arbitrary  standards  set 
up  and  preserved  by  the  various  standardising 
institutions.  The  kinetic  theory  of  gases 
and  the  law  of  the  equipartition  of  energy 
give  a  perfectly  definite  meaning  to  the  word, 
and  fixes  one  rational  thermometric  scale, 
known  as  the  thermodynamic  or  absolute 
scale,  which  does  not  differ  seriously  from 
the  earlier  thermometric  scales  on  the  one 
hand  or  on  the  other  from  what  might  be 
regarded  as  the  natural  meaning  of  the  word 
temperature,  or  intensity  of  heat,  impossible  as 
that  is  yet  to  define.  This  truly  remarkable 
coincidence  of  the  old  thermometric  scales 
with  the  thermodynamic  scale,  and  with 
the  true  scale,  when  we  are  in  a  position  to 
define  it,  has  had,  of  course,  great  practical 
advantages.  But  they  have  been  more  than 
counterbalanced  by  the  confusion  on  the 
philosophical  side  that  has  resulted  by  the 
use  of  a  term,  as  a  strictly  scientific  term, 
long  before  it  had  a  single  unchanging  mean- 
ing. 

The  scale  we  are  about  to  set  up,  the 
thermodynamic  scale,  is  in  a  sense  an  arbi- 
trary scale  like  its  predecessors.  Its  connec- 
tion with  the  natural  scale  must  be  left  over 
for  future  discussion.  Its  basis  is  the  law 


86  MATTER  AND  ENERGY 

of  equipartition  of  energy.  Two  substances 
have  the  same  temperature  as  that  of  a  gas 
— and  therefore  according  to  Euclid's  axiom 
are  themselves  of  the  same  temperature — 
when  they  can  be  brought  into  thermal 
communication  with  this  gas  without  altering 
the  kinetic  energy  of  translation  of  its  mole- 
cules, that  is,  without  altering  its  pressure 
when  its  volume  is  kept  constant  or  its  volume 
when  its  pressure  is  kept  constant. 

This  basis,  which  rests  on  Davy's  neglected 
generalisation  in  1812,  that  the  laws  of 
communication  of  heat  are  precisely  the 
same  as  the  laws  of  communication  of  motion, 
affords  at  once  a  scale  of  temperature.  That 
temperature  will  be  twice  another,  at  which 
the  kinetic  energy  of  translation  of  the  mole- 
cules, or,  the  pressure  at  constant  volume,  of 
a  gas  is  doubled.  If  we  adopt  the  Centigrade 
scale  we  find  that  the  pressure  of  a  constant 
volume  gas  thermometer  increases  for  each 
increase  of  1°  C.  by  1 /273rd  of  the  pressure 
of  the  gas  at  0°  C.,  and  decreases  by  the 
same  amount  for  each  1°  C.  below  0°  C. 

In  consequence,  at  a  temperature  of  273°  C. 
the  pressure  of  the  gas  is  doubled,  at  546°  C. 
it  is  trebled,  whilst  at  819°  C.  it  is  quadrupled, 
and  so  on  without  limit  so  far  as  is  known. 
Conversely,  coming  down  the  scale,  the 


HEAT  AND  THEORY  OF  MATTER  87 

temperature  will  be  halved  at- 136.5°  C., 
whilst  at-273°  C.,  if  the  gas  did  not  liquefy, 
as  all  known  gases  do  before  this  temperature 
is  reached,  the  pressure  and  kinetic  energy  of 
the  molecules  would  be  reduced  to  nothing. 
The  molecules  would  be  absolutely  still 
and  therefore  absolutely  cold,  and  nothing 
can  be  conceived  to  be  colder.  In  other 
words,  the  absolute  zero  of  temperature 
is  273°  below  zero  on  the  Centigrade  scale. 
The  Absolute  Scale  of  Temperature,  as 
it  is  called,  is  thus  obtained  by  adding 
273°  to  the  temperature  expressed  in  degrees 
Centigrade. 

It  will  be  observed  that  there  is  nothing 
inferred  here  of  the  intensity  of  heat,  that 
is,  the  quantity  of  heat  energy  per  unit 
quantity  of  substance  which  is  implied  in 
the  natural  definition.  If  we  tried  to  follow 
such  an  idea  at  present  we  should  be  landed 
in  a  quagmire  of  difficulties,  sufficiently 
indicated  by  the  older  distinction  of  two 
kinds  of  "heat,"  "sensible  heat"  and  "latent 
heat."  Still  less  is  the  thermodynamic 
scale  referred  to  gases  because  they  are 
practically  perfect  or  ideal  thermometric 
substances.  Such  a  substance  would  be  in- 
creased in  temperature  by  twice  the  amount 
by  the  communication  of  two  units  of  heat 


88  MATTER  AND  ENERGY 

energy  as  it  would  be  by  the  communication 
of  one  unit  of  heat  energy.  This  would 
only  necessarily  be  true  if  all  the  heat  was 
employed  in  increasing  the  kinetic  energy  of 
translation  of  the  molecules,  that  is,  in 
raising  the  temperature.  In  this  sense  the 
common  gases  are  very  far  from  fulfilling 
the  condition  laid  down.  We  have  merely 
stretched  a  tight-rope  across  an  abyss  of 
uncertainty  to  gain  entrance  into  regions 
beyond,  because  the  progress  of  science  is 
rapidly  converting  that  tight-rope  into  a 
bridge,  with  handrail  complete  for  the  most 
timid  adventurer. 

The  extension  of  the  kinetic  theory  to 
liquids  was  one  of  the  great  advances  of  the 
closing  decades  of  the  last  century.  Liquids, 
we  have  seen^  result  by  condensation  from 
gases  when  the  mutual  tendency  to  draw 
together,  which  the  molecules  exhibit,  be- 
comes, by  the  lowering  of  the  temperature, 
able  to  control  the  kinetic  energy  of  the 
molecules  and  to  restrict  their  movements 
so  that  they  are  no  longer  able  to  wander 
freely  away  into  space.  The  essential  differ- 
ences between  the  liquid  and  gaseous  states 
are,  however,  confined  solely  to  an  exceedingly 
thin  skin  at  the  boundary  or  surface  of  the 
liquid.  Inside  the  liquid  an  unhampered 


HEAT  AND  THEORY  OF  MATTER  89 

independent  motion  of  the  molecules,  moving 
by  virtue  of  their  own  kinetic  energy,  and  not 
restricted  in  any  way  except  by  their  in- 
cessant mutual  encounters,  is  going  on  exactly 
the  same  as  in  gases.  The  molecules  are,  it 
is  true,  generally  much  more  closely  packed 
in  liquids  than  in  gases,  and  in  consequence 
they  collide  much  more  frequently.  The 
"free  path,"  as  it  is  called,  in  liquids,  or  the 
average  linear  distance  each  molecule  moves 
before  it  experiences  an  encounter  with 
another,  is  exceedingly  minute.  Even  in 
gases  under  standard  conditions  this  free 
path  is,  as  a  rule,  a  distance  below  the  micro- 
scopically visible.  In  consequence,  in  liquids 
the  molecules  move  in  very  zigzag  paths, 
being  perpetually  turned  back  the  way  they 
came,  and  having  to  traverse  great  distances 
without  moving  very  far  away  from  their 
starting-point,  so  that  in  spite  of  their  great 
velocities  they  do  not  diffuse  very  rapidly. 
It  might  be  supposed  that,  owing  to  the 
natural  tendency  of  the  molecules  to  draw 
together,  or  in  the  phraseology  of  the  day  to 
their  great  mutual  attraction  for  one  another, 
the  character  of  the  motion  in  liquids  must 
be  different  from  that  in  gases.  This  is  not 
the  case  inside  the  surface  skin.  In  the 
interior  the  so-called  attractions  are  uniform 


90  MATTER  AND  ENERGY 

in  all  directions  and  therefore  cancel  out. 
The  molecule  is  attracted  equally  in  all 
directions  at  once,  and  hence  its  motion  is 
precisely  the  same  whether  such  attractions 
are  supposed  to  exist  or  not.  It  is  only  at 
the  surface  that  the  state  of  liquids  is  essen- 
tially different  from  that  of  gases.  For  at  the 
surface  the  tendency  of  the  molecules  to  move 
together,  that  is,  inward,  is  quite  unbalanced 
by  any  compensating  tendency  to  move 
outward.  This  causes  at  the  surface  a  very 
strong  tendency  for  the  molecules  to  move 
towards  the  interior  of  the  liquid,  which  is 
called  Surface  Tension,  and  to  which  practi- 
cally all  the  properties  of  liquids,  in  so  far  as 
they  are  distinguished  from  gases,  are  due. 
Inside  all  is  freedom  of  movement,  a  mad 
rushing  hither  and  thither  of  an  altogether 
disconnected  swarm  of  molecules  moving 
in  every  direction  at  once,  colliding  and 
rebounding,  but  never  stopping.  In  liquids 
the  crowd  is  much  more  closely  packed,  and 
the  motion,  therefore,  is  even  more  chaotic 
than  in  gases;  but  otherwise  there  is  no 
difference.  Now  the  law  of  equipartition 
of  energy  states  that  in  any  such  system  of 
free  unhampered  and  independently  moving 
units,  incessantly  colliding  with  each  other, 
each  separate  molecule,  nay  more,  each 


HEAT  AND  THEORY  OF  MATTER  91 

independent  particle,  whatever  its  mass,  on 
the  average  must  possess  the  same  amount 
of  kinetic  energy.  This  amount  of  kinetic 
energy  at  0°  C.  is  precisely  that  possessed 
by  a  molecule  of  hydrogen,  weighing  3 
million-million-million-millionth  of  a  gram 
moving  at  a  speed  of  rather  more  than  a  mile 
a  second.  If  the  particle  weighed  a  milli- 
gram, the  total  distance  it  would  move  in  a 
second,  even  if  its  almost  infinitely  entangled 
zigzag  path  were  straightened  out,  would 
be  scarcely  visible  under  the  microscope,  so 
that  we  must  not  expect  weighable  quantities 
of  matter  immersed  in  a  fluid  to  move  about 
visibly.  But  what  if  we  deal  with  the 
smallest  particles  it  is  possible  to  see  under 
the  microscope?  Then  we  shall  see  what 
Robert  Brown,  all  unaware  of  its  true  and 
tremendous  significance,  first  saw  with  mortal 
eyes,  the  perpetual  motion  of  the  molecules, 
which  mathematical  physics,  following  Davy's 
dictum  and  regarding  molecules  as  freely 
moving  masses  had,  by  means  of  the  embrac- 
ing theorem  of  the  equipartition  of  energy, 
arrived  at  with  the  eye  of  faith. 

Of  course,  in  the  Brownian  movement  we 
only  see  the  effects  of  the  actual  mad  rush 
of  the  molecules  themselves.  The  smallest 
particle  visible  under  the  microscope  contains 


92  MATTER  AND  ENERGY 

millions  of  separate  molecules.  If  we  begin 
by  a  particle  visible  to  the  naked  eye  sus- 
pended in  a  fluid,  on  account  of  its  relatively 
large  size,  it  is  subjected  to  a  rain  of  impacts 
from  the  molecules  which  is  practically  equal 
on  all  sides  at  the  same  time  and  the  effects 
of  which  cancel  one  another  out,  so  that  the 
particle  remains  practically  at  rest.  But  if 
we  reduce  its  size  gradually,  so  making  it 
at  the  same  time  lighter  and  quicker  to 
respond  to  molecular  impacts,  we  shall  arrive 
at  a  point  at  which  the  molecular  impacts 
do  not  always  so  cancel  out.  At  one  instant 
more  molecules  may  hit  one  side  than  the 
opposite,  and  the  light  particle  will  instantly 
dart  off  in  the  appropriate  direction.  Before 
it  has  moved  an  appreciable  distance,  some 
other  combination  of  simultaneous  impacts 
will  have  occurred  and  the  direction  will 
change,  and,  in  the  end,  the  particle,  if  only 
small  enough,  will  never  be  for  a  moment 
still,  but  will  be  agitated  perpetually  by  the 
bombardment  to  which  it  is  on  all  sides  sub- 
jected by  the  invisible  swarm  of  molecules. 

Some  beautiful  experiments  of  M.  Perrin 
have  recently  subjected  this  Brownian  move- 
ment to  quantitative  investigation.  By  a 
simple  ingenious  process  of  fractional  cen- 
trifugalisation,  he  succeeded  in  preparing 


HEAT  AND  THEORY  OF  MATTER  93 

emulsions  of  gamboge  and  gum  mastic  in 
water,  the  particles  of  which  were  all  of  the 
same  size,  which  could  be  measured  under 
the  microscope.  From  the  size  and  density 
of  the  substance  the  weight  of  the  particle 
could  be  deduced.  By  the  aid  of  the  re- 
searches of  numerous  mathematical  physicists 
he  was  able  to  calculate  the  mean  kinetic 
energy  of  translation  from  the  results  of  his 
observations  of  the  movement  under  the 
microscope.  He  examined  particles  varying 
in  mass  over  a  range  of  60,000  to  1  and  found 
that  the  mean  kinetic  energy  was  independent 
of  the  mass,  and  was,  moreover,  the  same  as 
that  of  a  molecule  of  hydrogen  or  any  other 
gas  at  the  same  temperature.  The  largest 
particles  he  examined  were  just  visible  with 
a  simple  lens  in  sunlight,  and  weighed 
100,000,000,000  times  as  much  as  the  molecule 
of  hydrogen,  and  the  movement  of  such 
relatively  large  particles  is  small  and  sluggish. 
With  the  smallest  visible  particles  the  motion, 
or  rather  commotion,  is  extraordinarily  lively. 
What  then  must  be  the  character  of  the 
invisible  turmoil  going  on  in  the  actual 
molecules  of  every  drop  of  liquid  and  every 
part  of  the  atmosphere  around  us? 

Perpetual  motion,  proportional  in  magni- 
tude to  the  square  root  of  the  absolute  tern- 


94  MATTER  AND  ENERGY 

perature  of  the  substance,  is  the  universal 
condition  of  the  liquid  and  the  gaseous 
states.  As  regards  the  solid  state  far  less  is 
known.  It  seems  clear  that  any  freedom  of 
translatory  motion  is  an  impossibility  for  a 
crystalline  solid,  for  the  crystal  form  is  the 
outcome  of  the  molecules  occupying  definite 
geometrical  positions  in  space  with  reference 
to  each  other.  But  vibratory  motion  in 
constrained  paths  there  must  be  among  the 
molecules  of  a  solid,  increasing  with  the 
temperature  until  the  molecules  drag  their 
anchors,  as  it  were,  and  the  substance  melts. 

What  inexhaustible  energy — the  waste 
energy  of  heat  of  uniform  temperature — 
these  molecules  everywhere  around  us  pos- 
sess! But  the  second  law  of  the  Doctrine  of 
Energy  states  that  this  source  of  energy  must 
for  ever  remain  useless  for  us.  Still  the  mind 
is  not  satisfied,  and  again  it  asks  for  the  reason. 

Let  us  consider  the  process  of  the  conver- 
sion of  the  energy  of  mechanical  motion  into 
the  energy  of  heat,  by  resistance  or  friction, 
and,  to  take  a  simple  case,  suppose  that 
water  is  spinning  round  or  rotating  in  a  pail. 
A  cork  floating  on  the  surface  or  a  ball  of  the 
right  specific  gravity  floating  below  the 
surface  moves  with  the  water  as  it  rotates. 
Its  motion  becomes  slower  and  slower  and 


HEAT  AND  THEORY  OF  MATTER  95 

finally  ceases.  At  first,  superimposed  on 
the  mad  rush  of  the  molecules  in  every  con- 
ceivable direction  at  once,  was  a  directed 
motion  of  the  mass  as  a  whole,  each  portion 
having  a  definite  resultant  motion  in  a  circu- 
lar path  around  the  centre  of  the  pail.  At  the 
end,  when  all  is  still,  we  know  that  although 
the  cork  or  floating  ball  remains  still,  the 
mad  motion  of  the  molecules  endures.  A 
suspended  particle  sufficiently  small  will 
show  the  Brownian  movement  anywhere  in 
the  liquid.  The  mechanical  energy  of  the 
originally  moving  water  has,  we  know,  been 
frittered  down  into  heat,  with  the  con- 
sequence that  the  temperature  and  hence 
the  separate  motions  of  the  individual  mole- 
cules has  been  increased  to  an  infinitesimal 
extent.  In  other  words,  the  directed  or  co- 
ordinated motion  of  the  mass  as  a  whole  has 
been  converted  by  the  process  into  the  per- 
fectly mad  or  decoordinated  motion  of  the 
individual  molecules.  The  motion  and  the 
energy  of  the  motion  has  not  been  destroyed. 
It  has  merely  been  divided  up  amongst  the 
smallest  particles,  all  sense  of  the  original 
direction  being  lost  and  a  perfectly  uniform 
distributed  motion  of  all  the  particles  in  all 
possible  directions  having  taken  its  place. 
The  conversion  of  mechanical  energy  into 


96  MATTER  AND  ENERGY 

heat  by  friction  involves  only  loss  of  direction 
and  of  co-ordination.  The  kind  of  perpetual 
motion  which  is  not  only  possible,  but  which, 
indeed,  is  the  only  universal  condition  of 
matter,  is  the  perfectly  useless  decoordinated 
motion  of  swarms  of  molecules.  The  kind 
of  perpetual  motion  which  is  impossible  in 
the  real,  as  contrasted  with  the  "ideal" 
world,  is  the  motion  which  retains  its  direc- 
tion unimpaired.  The  problem  of  achieving 
perpetual  motion  contrary  to  the  second  law 
is  that  of  bringing  order  and  direction  once 
more  into  the  chaotic  rush  of  the  molecules, 
to  marshal  and  drill  the  mob  so  that  once 
more  they  can  act  together  to  produce  a  com- 
mon effect. 

If  an  insight  has  been  obtained  into  the 
general  nature  of  the  Second  Law  of  Thermo- 
dynamics, its  quantitative  aspect,  which  is  of 
the  utmost  practical  importance  in  engineer- 
ing science,  will  not  prove  altogether  un- 
intelligible. Heat  at  the  uniform  temperature 
of  the  surroundings  cannot  practically  be 
transformed  into  mechanical  work,  although 
theoretically  this  might  be  accomplished  by 
the  operation  of  an  intelligence  directing  and 
regulating  the  traffic,  as  it  were,  among  the 
individual  molecules.  If  heat  were  so  trans- 
formed, the  substances  in  which  it  was  con- 


HEAT  AND  THEORY  OF  MATTER  97 

tained  would  be  cooled  to  a  lower  tem- 
perature than  before  to  an  extent  directly 
dependent  upon  the  amount  transformed. 
The  second  law  states  that  such  spontaneous 
cooling  below  the  temperature  of  the  sur- 
roundings is  not  possible.  The  various 
refrigerating  machines  which  practically  effect 
cooling  do  so  paradoxically  by  converting 
mechanical  work  into  heat,  and  later  a  simple 
case  of  such  a  cooling  will  be  considered. 

Spontaneous  cooling  of  a  substance  can 
only  occur  continuously  without  the  per- 
formance of  work  when  the  surroundings  are 
at  a  lower  temperature  than  the  substance. 
This  cooling  may  occur  in  a  perfectly  natural 
manner  by  means  of  simple  conduction  of 
heat,  in  which  case  all  of  the  heat  energy 
given  out  by  the  hot  substance  still  remains 
as  heat  energy  in  the  surroundings  at  the 
lower  temperature;  or  the  fall  of  the  tem- 
perature of  the  working  substance  may 
occur  in  an  artificial  or  directed  manner 
through  an  engine  which  transforms  a  part 
of  its  heat  energy  into  work,  so  that  only 
a  portion  of  the  heat,  the  untransformed 
portion,  remains  in  existence  after  the  cooling 
has  occurred  to  lower  the  temperature.  It  is 
possible  to  direct  and  regulate  the  flow  of 
heat  among  masses  of  matter  but  not  among 


98  MATTER  AND  ENERGY 

molecules.  The  mechanism  of  the  conver- 
sion will  be  considered  in  the  next  chapter. 
If  we  try  to  imagine  a  complete  conversion 
into  work  of  the  whole  of  the  heat  energy 
contained  in  a  certain  quantity  of  substance, 
we  see  at  once  that  thereby  the  temperature 
of  that  substance  must  be  reduced  to  the 
absolute  zero, —273°  C.  The  process  of 
cooling,  however,  stops  naturally  when  the 
temperature  reached  becomes  that  of  the  sur- 
roundings. Thus,  if  we  consider  a  simple 
substance  cooling  without  any  change  of 
state,  the  heat  it  will  evolve  in  cooling  any 
number  of  degrees  is  only  a  part  of  its  total 
heat  energy,  and  this  part  is  calculable.  If 
it  cools  from  100°  to  0°  C.,  this  is  from  373° 
to  273°  absolute,  the  proportion  of  the  heat 
energy  remaining  in  the  substance  after 
cooling  to  that  initially  present  is  as  273  to 
373,  so  that  the  proportion  that  has  left  the 
substance  is  100/373  of  the  amount  initially 
present,  or  100/273  of  the  amount  finally 
present.  This  fraction  100/373  of  the  initial 
heat,  in  the  example  chosen,  is  all  that  leaves 
the  substance,  and  therefore  is  the  maximum 
available  for  conversion  into  work.  So  that  if 
a  perfect  transformation  of  this  portion  into 
work  were  possible,  the  efficiency  of  the 
process  would  still  be  only  about  27%. 


HEAT  AND  THEORY  OF  MATTER  99 

Whereas  of  an  electric  motor  an  efficiency  of 
90  to  95%  is  expected,  that  is,  it  will  trans- 
form this  fraction  of  the  electrical  energy 
supplied  to  it  into  mechanical  work  under 
proper  conditions.  We  can  increase  the 
efficiency  of  the  transformation  of  heat  into 
work  in  only  two  ways.  The  first  is  to  lower 
the  final  temperature  attained,  which  is 
impossible,  practically,  as  the  final  tem- 
perature is  fixed  as  the  prevailing  tempera- 
ture of  the  earth  and  air.  The  second  is  to 
increase  the  initial  temperature.  Obviously 
the  higher  the  initial  temperature  the  greater 
the  proportion  of  heat  available  for  trans- 
formation. For  this  reason  gas  and  oil 
engines,  which  work  between  wider  limits 
of  temperature  than  the  steam  engine,  are 
thermodynamically  much  more  efficient.  It 
might  be  thought  that  these  simple  considera- 
tions, so  easily  understood  when  one  deals 
with  a  substance  cooling  without  change  of 
state,  might  not  apply  to  the  case  where,  as 
in  the  steam  engine,  changes  of  state  from 
liquid  to  vapour  and  from  vapour  back  into 
liquid  occur.  Experience  proves  that  they 
do  apply. 

The  relation  already  deduced  between  the 
initial  and  final  temperatures  and  the  maxi- 
mum possible  efficiency  of  the  conversion  pro- 


100          MATTER  AND  ENERGY 

cess  is  of  perfectly  general  applicability,  and 
so  far  as  is  known  is  universally  true  of  all 
artificial  heat  engines.  If  T!  is  the  absolute 
temperature  of  the  source  of  heat,  or  boiler, 
and  T2  that  of  the  reservoir  of  heat,  or 
condenser,  the  possible  efficiency  of  the 
process,  or  the  ratio  between  the  quantity 
of  work  produced  and  the  quantity  of  heat 
supplied,  is  Tj-Tg/Tj.  It  is  hardly  necessary 
to  say  that  this  maximum  theoretical  effi- 
ciency is  not  even  approximated  to  in 
any  actual  engine,  not  through  any  fault 
of  the  engineers,  but  because  the  ideal 
theoretical  conditions  are  entirely  different 
from,  and  in  many  cases  diametrically 
opposed  to,  those  obtaining  in  practice. 

The  question  may  now  be  asked  whether 
the  limitation  expressed  by  the  second  law 
is  necessarily  and  permanently  true,  or 
whether  it  is  merely  an  expression  of  the 
fact  that,  so  far,  no  process  has  been  dis- 
covered competent  to  bring  order  and  direc- 
tion into  the  chaotic  rush  of  molecules. 
As  has  always  been  understood  by  the  best 
exponents  of  the  law,  the  existence  of  any 
sort  of  "molecular  intelligence"  would  vitiate 
the  second  law.  For  though,  throughout, 
we  have  spoken  of  mean  velocity,  mean 
kinetic  energy,  etc.,  as  the  statistical  averages 


HEAT  AND  THEORY  OF  MATTER  101 

applying  to  the  whole  immense  swarm  of 
molecules,  averages  which  have  perfectly 
definite  values,  the  individual  molecules  in 
the  same  mass  of  matter  depart  from  these 
average  values  widely.  In  a  gas  at  uniform 
temperature  some  small  proportion  of  the 
whole  are  moving  with  speeds  many  times 
greater  than  the  average  speed,  and  some 
small  proportion  at  speeds  many  times  less 
than  the  average.  Even  if  all  the  molecules 
began  at  the  same  speed,  the  incessant 
collisions  among  them  would  at  once  result 
in  inequalities.  There  is  a  perfectly  definite 
distribution  of  velocity,  and  the  fraction  of 
the  total  number  of  molecules  actually 
possessing  the  mean  velocity,  or  any  assigned 
velocity  above  or  below  this  mean,  can  be 
calculated  perfectly  satisfactorily.  Hence  in 
a  gas  of  uniform  temperature  there  are, 
from  a  molecular  point  of  view,  wide  varia- 
tions of  temperature,  and  there  seems  no 
reason  why,  for  example,  molecules  should 
not  in  some  cases  be  able  to  utilise  this,  to 
them,  available  energy  and  convert  it  into 
other  forms  available  for  the  larger  world. 

The  question  has  often  been  mooted,  for 
example,  whether  the  processes  of  life  obey 
the  second  law.  Certainly  from  some  points 
of  view  a  horse  or  other  beast  of  burden 


102  MATTER  AND  ENERGY 

is  an  extraordinarily  efficient  machine,  as 
Count  Rumford  perfectly  well  knew.  How 
efficient,  possibly  was  not  generally  realised 
until  motor  cars  came  in,  and  instead  of 
two  horses  to  pull  the  car  it  was  found,  in 
the  absence  of  a  whip,  that  twelve  or  fifteen 
was  an  appropriate  minimum  number,  or 
the  car  would  stick  on  every  moderate  hill. 
The  so-called  horse-power,  which  furnishes 
the  engineer's  unit,  is  not  the  power  of  an 
ordinary  horse  either,  but  was  fixed  by 
tests  on  the  best  British  cart  horses  which 
could  be  procured.  Have  the  minute  cells 
of  the  body  the  power  of  taking  advantage 
of  the  difference  in  the  temperature  of  the 
molecules  bombarding  them,  and  when  one 
comes  along  at  more  than  average  speed, 
absorbing  it  and  its  energy,  building  up  a 
larger  cell  thereby,  which  in  course  of  time 
undergoes  metabolism  and  evolves  again  its 
store  of  energy?  It  is  a  fascinating  and  a 
legitimate  line  of  inquiry,  but  time  alone 
and  experiment  will  answer  it  decisively. 
With  the  full  understanding  that  the  second 
law  merely  states  that  it  is  impossible  usefully 
to  direct  the  chaotic  movements  of  molecules 
or  to  co-ordinate  them,  respect  for  it  as 
one  of  the  necessary  fundamental  laws  of 
science  will  be  weakened  and  applications 


HEAT  AND  THEORY  OF  MATTER  103 

of  it  to  entirely  unknown  phenomena  only 
made  with  caution. 

Particularly  where  intelligence  operates  is 
this  the  case.  Life  in  its  lowliest  is  a  single 
cell,  vastly  complex,  it  is  true,  from  the  mo- 
lecular point  of  view,  but  still  small  enough 
to  be  agitated  by  the  Brownian  movement. 
Brown  actually  thought,  when  he  discovered 
the  phenomenon  called  by  his  name,  that 
the  particles  he  was  observing  were  alive, 
so  closely  does  their  motion  simulate  that 
of  the  smallest  organisms.  If  life  begins 
with  a  single  cell,  does  intelligence?  Does 
the  physical  distinction  between  living  and 
dead  matter  begin  in  the  jostling  molecular 
crowd?  Inanimate  molecules  in  all  their 
movements  obey  the  law  of  probability,  the 
law  which  governs  the  successive  falls  of  a 
true  die.  In  the  presence  of  a  rudimentary 
intelligence  do  they  still  follow  the  law,  or 
do  they  now  obey  another  law,  the  law  of  a 
die  that  is  loaded?  If  so,  mathematicians 
will  have  to  extend  their  investigations  to 
cases  where  the  laws  of  simple  probability 
do  not  act  alone,  and  their  domain  to  fields 
into  which  they  have  not  hitherto  entered. 
For  the  living  body  is,  after  all,  a  machine 
first.  We  know  machines  that  are  without 
life,  but  we  do  not  know  life  apart  from  its 


104  MATTER  AND  ENERGY 

machine.  The  modern  world,  which  has 
recently  learned  that  it  is  useless  to  try  to 
educate  a  child  that  is  not  fed,  has  had  its 
attention  directed  somewhat  forcibly  to  this 
aspect  of  life. 

The  suggestion  just  made  is,  however,  but 
one  of  many  views  worth  discussing.  Another 
is  that  life  processes  do  not  obey  the  second 
law,  for  there  seems  to  be  a  consensus  of 
opinion  that  they  cannot  possibly  obey  it, 
because  the  chemical  energy  of  food  suffers 
direct  transformation  into  work  without 
first  being  converted  into  heat.  As  will 
later  be  discussed,  the  second  law  would 
not  then  operate.  Now  this  is  just  another 
problem  which  is  of  immense  practical 
importance.  Many  chemical  changes  can 
be  made  to  take  place  in  such  a  way  as  to 
yield  their  energy  not  as  heat,  but  as  elec- 
trical energy  directly.  But  such  a  result 
for  the  most  important  of  all  chemical 
changes,  that  equivalent  to  the  combustion 
of  fuel,  has  not  so  far  been  achieved.  Be 
the  explanation  what  it  may,  the  living  body 
is  an  extraordinarily  efficient  machine,  not 
so  much  on  the  side  of  the  absolute  value 
of  its  efficiency,  of  which,  indeed,  far  too 
little  is  known,  but  because  it  deals  with 
kinds  of  chemical  change  which  cannot  be 


CHEMICAL  ENERGY  105 

converted  by  inanimate  engines  into  useful 
forms  of  energy  without  terrible  waste. 


CHAPTER  V 

POTENTIAL  AND   CHEMICAL  ENERGY 

IT  is  curious  to  reflect  upon  the  reason 
why  mechanics  was  an  exact  science  from 
the  time  of  Newton  for  nearly  two  centuries 
before  the  doctrine  of  the  conservation  of 
energy  was  established.  Newton  in  his  first 
law  of  motion  stated  an  hitherto  unrecog- 
nised great  truth.  The  natural  and  simplest 
kind  of  motion  is  uniform  continuous  motion. 
This  simple  uniform  continuous  motion, 
unchanged  in  amount  or  direction,  is  never 
realised  practically  except  among  the  stars. 
In  no  other  case  is  motion  entirely  free  and 
unhampered.  On  the  earth,  friction  and  the 
resistance  offered  by  the  air  gradually  reduce 
a  moving  body  to  the  state  of  rest.  The 
velocities  of  the  planets,  whilst  they  remain 
sensibly  uniform  in  amount,  change  their 
direction  unceasingly  and  follow  circular 
rather  than  straight  paths,  because  the 


106  MATTER  AND  ENERGY 

planets  are  not  alone  in  space,  but  are  in 
proximity  to  a  much  larger  sun,  towards 
which  their  motion  tends.  In  empty  space 
a  mass  of  matter,  if  moving  initially,  moves 
on  unchanged  in  direction  or  speed  for  ever 
and  ever,  and  Newton  was  the  first  to  recog- 
nise it.  In  dealing  with  actual  cases  of 
motion  in  the  heavens  and  earth,  Newton 
fell  into  the  common  error  of  his  day.  He 
imagined  causes  to  exist  for  the  departure 
of  these  motions  from  the  natural  or  simple 
law,  and  it  has  taken  science  three  centuries 
to  recognise  that  the  causes  imagined  are 
not  real  causes,  and  that  they  only  describe 
the  effects,  without  any  more  light  upon  the 
origin  of  these  effects.  The  imaginary  cause 
of  change  of  motion,  Newton  defined  as 
Force.  Great  men  have  more  to  fear  from 
their  followers  than  from  their  opponents,  for 
Newton's  mind  was  such  that  it  is  impossible 
that  he  himself  could  have  remained  long 
under  any  misunderstanding  as  to  what 
Force  really  was.  The  universal  attribute 
of  matter,  whereby  it  gravitates,  was  ac- 
counted for  by  imagining  that  all  matter 
attracted  all  other  matter  with  a  force  which 
was  termed  the  force  of  gravity.  The  law 
of  gravitation  stated  that  the  force  of  gravity 
varies  according  to  the  product  of  the  masses 


CHEMICAL  ENERGY  107 

of  the  matter  gravitating,  and  inversely 
according  to  the  square  of  their  distance 
apart.  No  exception  can  be  taken  to  this 
view  as  long  as  it  is  recognised  clearly  that 
it  expresses  simply  that  the  motions  which 
matter  executes  in  space  are  what  they  would 
be  supposing  the  force  of  gravity  obeying 
the  law  stated  did  exist.  But  whenever 
the  motion  of  matter  departs  from  the 
simple  law,  appropriate  forces  have  been 
imagined  to  exist.  Thus  in  the  condensation 
together  of  the  molecules  of  a  gas  to  form  a 
liquid  the  molecules  are  imagined  to  attract 
one  another.  The  property  of  the  electric 
charge  of  spontaneously  dissipating  itself 
so  that  it  always  resides  on  the  surface  of 
a  charged  body,  is  spoken  of  as  being  due 
to  the  repulsion  of  similar  electric  charges. 
Atoms  of  matter  are  regarded  as  attracting 
or  repelling  one  another  with  the  force  of 
chemical  affinity,  a  phrase  which  makes 
every  thinking  man  shudder.  So  has  grown 
up  the  preposterous  notion  that  forces  really 
exist  and  are  the  permanent  attributes  of 
masses  of  matter,  molecules,  atoms,  elec- 
tricity, etc.  When  a  weight  rests  upon  the 
table  the  force  of  gravity  is  supposed  to  be 
"acting"  all  the  time.  The  earth  is  regarded 
as  attracting  it  with  a  constant  pull,  and 


108  MATTER  AND  ENERGY 

the  "reaction"  of  the  table  prevents  the 
weight  falling.  This  is  not  the  proper  view 
to  take.  It  is  true  that  in  the  science  of 
mechanics,  where  gravitation  is  the  dominat- 
ing phenomenon,  it  is  convenient.  But  the 
conception  of  force  and  its  pseudo-physical 
reality  undoubtedly  delayed  for  centuries 
the  recognition  of  the  law  of  the  conserva- 
tion of  energy.  Only  what  is  conserved  has 
the  right  to  be  considered  a  physical  existence. 
Long  and  mistaken  were  the  attempts  to 
arrive  at  a  conservation  of  forces.  In  other 
branches  of  science  the  conception  of  force 
is  a  stumbling-block  and  a  delusion.  The 
purest  example  of  motion  according  to  the 
first  law  is  the  motion  at  constant  tempera- 
ture of  molecules  of  a  gas  taken  as  a  whole. 
It  is  true  that  the  direction  of  motion  is  un- 
ceasingly changing  by  impacts  of  the  mole- 
cules upon  the  walls  of  the  containing  vessel 
and  by  mutual  collisions  between  the  mole- 
cules. Interchange  of  motion,  and  therefore 
of  the  kinetic  energy  of  motion,  is  always 
going  on.  But  considered  statistically,  that 
is,  keeping  in  mind  only  the  average  motion 
of  the  molecules,  or  their  total  kinetic  energy, 
no  change  results  as  a  consequence  of  these 
countless  collisions.  Thousands  of  millions 
of  times  a  second  for  each  molecule  encounters 


CHEMICAL  ENERGY  109 

occur,  reversing  or  altering  the  direction  of 
the  molecules.  According  to  the  definition 
of  "  force,"  intermittent  "  forces "  come 
into  play  thousands  of  millions  of  times  a 
second  and  disappear,  just  as  in  the  collision 
of  billiard  balls.  Whereas,  since  two  mole- 
cule or  billiard  balls  cannot  occupy  the  same 
space  at  the  same  time,  it  is  more  natural 
in  such  cases  not  to  invent  "forces"  between 
the  molecules  to  account  for  their  departure, 
as  individuals,  from  the  law  of  simple  uniform 
motion,  so  making  them  appear  to  exert 
forces  rather  than  to  pursue  the  easiest 
paths  available.  It  is  sufficient  simply  to 
regard  the  twists  and  turns  of  their  motion 
as  due  to  their  relative  position. 

Then  the  truth  emerges  that  all  so-called 
forces  are  positional.  Whether  anything 
"attracts"  or  "repels"  another  is  a  question 
not  only  of  the  nature  of  the  "attractor" 
and  "attracted,"  but  also  of  their  relative 
position.  The  fact  that  by  no  means  can 
we  put  ourselves  into  a  position  not  dominated 
by  the  effects  of  gravitation,  led  erroneously 
to  the  idea  that  forces  still  act  even  when 
they  produce  no  effects.  It  is  contrary  to 
the  spirit  of  modern  science  to  imagine  the 
existence  of  causes  which  in  reality  are 
names  only,  and  which  throw  no  light  at  all 


110          MATTER  AND  ENERGY 

on  the  effects  they  are  supposed  to  explain. 
Yet  we  still  speak  of  things  attracting,  repel- 
ling and  exerting  forces  as  if  they  were 
actual  agents.  We — in  our  anthropomorphic 
fashion — invest  them  with  human  attributes, 
just  as  the  Greeks  invested  their  gods. 

The  reason  is  that  the  English  language 
is  quite  unable  to  express  motion,  other 
than  that  according  to  the  first  law,  except 
by  words  implying  cause.  We  have  to  say 
two  bodies  attract  and  repel  one  another 
when  we  mean  that  they  naturally  tend  to 
approach  or  to  move  away  from  one  another, 
and  if  no  obstacle  stands  in  the  way,  do  so 
move.  The  words  "attract"  and  "repel" 
have  no  intransitive  forms  to  express  the 
effects  of  which  they  themselves  signify  the 
cause.  Unless  these  terms  are  coined,  the 
language  fails  to  express  the  ideas  of  science. 
There  is  one  word,  "to  gravitate,"  which 
simply  expresses  motion  of  a  particular  kind 
without  implying  any  idea  of  cause.  So  let 
us  invent  the  terms  "to  tractate"  and  "to 
pel  late"  when  otherwise  we  should  be  forced 
to  employ  "attract"  or  "repel,"  and  speak 
of  bodies  "tractating"  and  "pellating" 
when  otherwise  it  would  be  necessary  to  say 
that  one  body  attracts  or  repels  the  other. 

When  the  tractation  or  pellation  is  over, 


CHEMICAL  ENERGY  111 

no  imaginary  forces  remain  to  bother  about, 
for  these  terms  express  processes  rather  than 
their  unknown  causes.  But  •  these  natural 
processes  may  be  reversed.  Bodies  which 
tractate  may  be  made  to  move  farther 
apart,  and  this  must  therefore  be  termed 
"detractation,"  the  moving  apart  of  bodies 
which  naturally  approach.  Similarly  we 
have  "depellation,"  the  moving  together  of 
bodies  which  naturally  move  apart.  So 
equipped,  we  may  now  hope  to  consider 
some  phenomena  where  motion  is  not  the 
simple  motion  according  to  Newton's  first 
law,  but  depends  upon  the  position  of  the 
moving  bodies  relatively  to  one  another.  In 
other  words,  we  pass  from  the  consideration 
of  kinetic  energy  to  that  of  potential  energy. 
In  tractation  or  pellation,  bodies  spontane- 
ously draw  together  or  draw  apart,  even 
though  at  rest  initially,  and  acquire  therefore 
kinetic  energy.  In  each  process  the  appear- 
ance of  kinetic  energy  accompanies  the 
change  of  position.  Hence  the  bodies  in 
their  original  position,  though  possibly 
possessing  no  kinetic  energy,  have  energy — 
if  energy  is  real  and  not  a  delusion — which  is 
associated  with  their  position.  This  is  what 
is  meant  by  potential  energy.  Tractation 
and  pellation  may  therefore  be  defined  both 


112          MATTER  AND  ENERGY 

as  processes  in  which  energy  of  position 
is  converted  into  energy  of  motion,  in  the 
first  case,  by  the  shrinkage  or  concentration, 
in  the  second  case,  by  the  expansion  of  the 
parts  of  the  system. 

It  may  be  said  at  once  that  potential  energy 
is  a  way  of  expressing  facts,  not  supposed 
explanations  of  them.  Why  two  bodies 
tractate  or  pellate  is  not  known  in  a  single 
instance,  least  of  all  perhaps  in  the  oldest 
recognised  case,  gravitation.  An  ingenious 
theory  of  gravitation  was  put  forward  a 
century  ago  which,  though  not  accepted,  is 
very  suggestive,  and  illustrates  the  difference 
between  what  science  would  consider  a  real 
cause  and  one  that  is  fictitious,  like  the 
"force  of  gravity."  Le  Sage  imagined  that 
all  space  was  filled  with  "ultra-mundane 
corpuscles,"  or  particles  smaller  than  mate- 
rial particles,  flying  about  in  all  directions, 
moving  in  straight  lines  according  to  the 
first  law  of  motion,  and  possessing  kinetic 
energy.  A  single  world  in  space  is  subjected 
to  the  rain  of  these  corpuscles  from  all  direc- 
tions at  once,  and  so  remains  still.  Two 
worlds  in  space  both  are  similarly  bombarded, 
but  each  screens  the  other  from  the  particles 
coming  in  a  particular  direction,  and  so  they 
are  urged  towards  each  other!  Such  explains 


CHEMICAL  ENERGY  113 

beautifully  one  part  of  the  law  of  gravitation, 
that  the  effect  decreases  as  the  square  of  the 
distance  apart  of  the  bodies.  But  it  would 
be  natural  to  suppose  that  the  area  rather 
than  the  mass  of  the  body  would  condition 
its  screening  effect. 

Le  Sage  and  Newton  both  "imagined,"  but 
the  former's  hypothesis  is  no  verbal  restate- 
ment of  the  effect.  It  traces  gravitation  to 
imaginary  corpuscles,  but,  if  it  is  correct, 
these  corpuscles  are  real.  So  long  as  gravita- 
tion is  the  only  effect  these  corpuscles  pro- 
duce, and  so  long  as  they  remain  unknowable 
apart  from  gravitation,  the  two  explanations 
are  on  a  par.  But  if  such  corpuscles  are  real 
they  should  ultimately,  as  science  advances, 
become  knowable,  and  hence  the  truth  of 
the  explanation  can  be  examined.  In  this 
sense  it  is  an  attempt  to  find  a  real  cause. 
Science  of  the  last  decade  has  moved  very 
near  Le  Sage's  conceptions.  We  know  rays — 
the  7-rays  of  radium — which  penetrate  several 
inches  of  lead  before  they  are  stopped,  and 
which  are  supposed  by  some  to  be  corpuscles 
or  particles  smaller  than  atoms.  But  the 
difficulties  as  well  as  the  possibilities  of  this 
view  of  gravitation  have  also  been  thereby 
increased.  The  value  of  the  hypothesis  is  that 
it  gives  us  in  one  case,  if  we  accepted  it,  an 


114          MATTER  AND  ENERGY 

idea  of  what  potential  energy  might  be, 
namely,  the  kinetic  energy  of  what  has  so 
far  remained  outside  the  ken  of  science. 

Frankly  it  must  be  admitted,  however, 
that  the  real  causes  of  tractation  and  pella- 
tion  are  unknown,  though  not  necessarily 
unknowable.  That  being  so,  we  accept  the 
observed  phenomena  as  facts,  and  find  out 
all  we  can  as  to  how  they  operate,  and  in  this 
field  much  is  known.  The  case  of  the  tracta- 
tion of  steam  into  water  and  of  the  pellation 
of  water  into  ice  has  already  been  referred 
to.  When  the  molecules  of  the  gas,  steam, 
are  compressed  or  crowded  together  to  an 
extent  which  must  be  the  greater  the  higher 
the  temperature,  the  steam  condenses  into 
water  without  change  of  temperature,  but  a 
large  amount  of  heat,  the  so-called  latent 
heat  of  condensation,  is  produced.  If  this 
is  not  allowed  to  escape,  the  condensation 
stops.  The  heat  generated  will  not  raise  the 
temperature  of  the  steam,  even  if  it  is  not 
got  rid  of.  Neither,  when  the  heat  is  allowed 
to  escape,  does  the  temperature  of  the  steam 
fall,  so  long  as  any  remains  uncondensed. 
Conversely  when  steam  is  raised  from  water, 
at  a  temperature  which  must  be  the  higher 
the  greater  the  pressure,  the  molecules  of  the 
liquid  are  changed  into  molecules  of  the  gas, 


CHEMICAL  ENERGY  115 

and  a  great  amount  of  heat — the  latent 
heat  of  vaporisation — is  absorbed  without 
increasing  the  temperature.  The  difference 
between  tractation  and  pellation  and  simple 
concentration  or  expansion  is  that  kinetic 
energy  appears  invariably  as  the  result  of  the 
change  of  position.  A  perfect  gas,  and  the 
same  is  nearly  true  of  the  common  gases, 
neither  tractates  nor  pellates.  Whereas  con- 
densation of  a  gas  to  a  liquid  is  invariably 
a  tractation,  whilst  the  formation  of  a  gas 
from  a  liquid  is  a  detractation.  In  the  first 
kinetic  energy  appears  as  the  so-called  latent 
heat  of  condensation,  in  the  second  kinetic 
energy  disappears,  and  this  disappearance 
is  termed  the  latent  heat  of  vaporisation. 
This  confusing  term,  "latent  heat,"  does 
not  express  heat  at  all,  but  the  change  of 
energy  of  motion  (heat)  into  energy  of  posi- 
tion, or  vice  versa.  The  heat  energy  of  the 
molecules  is  the  same  whether  the  molecules 
are  liquid  or  gaseous,  but  the  latter  have,  in 
addition,  energy  of  position.  When  they 
condense  to  form  a  liquid,  kinetic  energy  is 
evolved.  In  the  freezing  of  water  into  ice 
the  molecules  pellate  and  acquire  kinetic 
energy  (latent  heat  of  liquefaction),  which 
must  be  removed  before  the  freezing  can 
continue.  In  the  melting  of  ice  into  water 


116          MATTER  AND  ENERGY 

the  molecules  depellate,  and  kinetic  energy 
or  heat  disappears  (latent  heat  of  fusion). 
These  simple  cases  show  that  a  pellation  is 
not  merely  the  opposite  of  tractation,  i.e.  a 
detractation.  If  the  freezing  of  water  were 
a  detractation,  kinetic  energy  or  heat  would 
be  absorbed  instead  of  being  set  free.  Water, 
however,  is  rather  exceptional,  and  the  usual 
behaviour  is  for  molecules  to  tractate  when 
they  pass  from  the  liquid  to  the  solid  phase, 
just  as  they  do  when  they  pass  from  the 
gaseous  to  the  liquid  phase.  Why  they  do 
so  may  be  imagined  but  not  demonstrated. 

As  explained  in  the  Volume  in  this  Library 
on  Astronomy  (p.  40),  the  tractation  or 
gravitation  of  the  matter  when  a  sun  shrinks 
may  convert  enormous  quantities  of  energy  of 
position  into  energy  of  motion  or  heat.  In  the 
tractation  of  masses  kinetic  energy  appears. 

In  the  tractation  of  molecules,  heat  results. 
No  machine  is  known  capable  of  employing 
the  tractation  of  the  molecules  to  produce 
mechanical  energy  directly.  Hence  all  heat 
machines,  whether  they  depend  on  tractation 
or  not,  obey  the  second  law.  The  kinetic 
energy  appears  first  as  an  increase  in  the 
uncoordinated  movements  of  the  molecules, 
and  can  only  be  partially  coordinated  for  any 
common  purpose. 


CHEMICAL  ENERGY  117 

Having  considered,  so  far,  what  the  second 
law  teaches,  it  will  be  instructive  to  refer  to 
a  common  error.  The  law  certainly  does 
not  state  that  none  of  the  heat  energy  of 
uniform  temperature  can  under  any  circum- 
stances be  converted  into  mechanical  energy. 
A  clear  picture  can  be  obtained  as  to  the 
actual  mechanism  in  any  heat  engine  by 
which  the  heat  is  converted  into  work. 

In  any  cylinder  and  piston  filled  with  a 
gas  or  vapour,  the  molecules  impinge  on  the 
fixed  walls  of  the  cylinder  and  on  the  station- 
ary piston  and  rebound  without  loss  of  energy 
like  the  perfectly  elastic  particles  they  are. 
But  if  now  the  piston,  under  the  impacts 
of  the  gas  molecules,  commences  to  move 
outward,  carrying  with  it  all  the  connected 
machinery,  part  of  the  thermal  energy  of  the 
flying  molecules  is  converted  into  mechanical 
energy,  and  the  gas  is  cooled.  The  molecules 
striking  the  receding  piston  do  not  rebound 
with  their  initial  energy  as  they  do  when 
they  strike  the  stationary  wall  of  the  cylinder, 
any  more  than  a  tennis  ball  received  by  the 
player  on  a  receding  racquet  rebounds  with 
the  same  energy  as  if  the  racquet  were  held 
rigidly.  Conversely  if  the  piston  is  entering 
the  cylinder,  compressing  the  gas,  the  mole- 
cules striking  it  rebound  with  more  than  their 


118  MATTER  AND  ENERGY 

initial  velocity,  and  the  gas  is  heated,  the 
energy  of  the  moving  machinery  now  being 
spent  in  heating  the  gas.  The  tennis  player, 
on  the  analogy,  now  advances  his  racquet 
to  meet  the  ball,  driving  it  back  with  more 
than  the  energy  with  which  it  was  approach- 
ing him. 

If  a  bottle  of  compressed  gas  is  opened,  the 
gas  rushes  out  into  the  air  and  does  work 
making  room  for  itself  and  forcing  the  sur- 
rounding atmosphere  out  of  the  way,  or  it 
may  be  used  to  force  out  the  piston  from  a 
cylinder.  It  cools  at  once,  and  the  bottle 
may  become  so  cold  that  the  moisture  of  the 
air  condenses  upon  it  as  snow.  Here,  then, 
is  a  case  where  we  start  with  everything  at 
the  uniform  temperature  of  the  surroundings, 
and  convert  part  of  the  heat  into  mechanical 
work,  cooling  the  substance  below  the  tem- 
perature of  the  surroundings.  If  we  had  done 
no  more  than  this  we  might  be  inclined  to 
think  that  the  second  law  could  not  be  true. 
As  a  matter  of  fact  the  jinnee  of  the  bottle 
has  been  allowed  to  escape.  We  have  let 
the  gas  expand,  and  to  compress  it  back  to 
its  original  volume  the  process  is  exactly 
reversed,  the  work  before  gained  is  all  spent 
and  converted  back  into  heat. 

The  principle  of  all  refrigerating  machines 


CHEMICAL  ENERGY  119 

will  now  be  clear.  Air  or  other  gas  or  vapour 
at  high  pressure  is  allowed  to  expand,  so 
doing  work  and  becoming  cold,  cooling  the 
substance  it  is  desired  to  freeze.  But  air 
at  high  pressure  is  not  a  natural  commodity, 
and  so  an  engine  is  first  employed  to  com- 
press the  air,  doing  work  on  it,  which  work  is 
turned  into  heat  and  the  air  becomes  hot. 
This  heat  is  removed  by  circulating  the 
compressed  air  through  cooling  tubes  im- 
mersed in  flowing  water,  and  the  cooled  com- 
pressed air,  when  now  allowed  to  expand, 
becomes  as  much  colder  than  its  surroundings 
as  it  became  hotter  when  compressed.  Para- 
doxically, refrigeration  is  effected  by  con- 
verting mechanical  energy  into  heat,  in  order 
to  be  able  to  reconvert  heat  back  into 
mechanical  energy  at  a  later  stage,  when  the 
working  substance  has  been  cooled  to  the 
temperature  of  the  surroundings.  The  second 
law  which  applies  to  the  whole  process  is 
therefore  borne  out  in  this  case. 

Imagine  a  tall  tank  filled  with  water 
reaching  from  the  lowest  hold  to  the  upper- 
most deck  of  a  liner.  Opening  a  hole  in  the 
bottom  of  the  vessel  beneath  the  tank  will 
effect  the  discharge  of  its  contents,  until  the 
water-level  in  the  tank  is  the  same  as  that 
of  the  surrounding  ocean.  Or,  if  the  tank 


120  MATTER  AND  ENERGY 

were  empty  to  start  with,  the  opening  of  the 
hole  would  cause  the  tank  to  fill  to  the  same 
level  as  before.  To  empty  the  tank  com- 
pletely or  to  fill  it  completely  requires 
pumping.  The  cooling  of  a  hot  substance 
or  the  heating  of  a  cold  one  are  natural  pro- 
cesses which  occur  spontaneously  like  the 
partial  emptying  or  the  partial  filling  of  the 
tank  considered.  The  heating  of  a  substance 
above  the  temperature  of  its  surroundings 
or  its  cooling  below  this  temperature  are  not 
natural  spontaneous  processes,  but  are  only 
to  be  effected  by  artificial  processes  analogous 
to  pumping.  The  whole  matter  is  summed 
up  in  the  statement  that  we  are  living  in  an 
immense  ocean  of  heat  energy  at  constant 
level,  and  efforts  to  raise  heat  above  or  depress 
it  below  this  level  are  no  more  to  be  thought 
of  without  the  expenditure  of  work  than  the 
elevation  or  depression  of  the  level  of  the  sea. 
Davy's  dictum  that  the  laws  of  communica- 
tion of  heat  are  precisely  the  same  as  the  laws 
of  communication  of  motion  is  still  the  best 
general  expression  of  the  reasons  underlying 
the  second  law. 

This  commentary  upon  the  molecular 
aspect  of  heat  would  be  unprofitable  if  it 
did  not  enable  certain  features  in  the  all- 
important  processes  of  thermodynamics  to 


CHEMICAL  ENERGY  121 

be  seen  more  clearly  than  the  more  formal 
presentations  allow.  By  the  law  of  the 
equipartition  of  energy  we  obtained  a  definite 
conception  of  temperature — at  least  of  tem- 
peratures referred  to  gases.  Temperatures 
on  this  scale  are  proportional  to  the  average 
kinetic  energy  of  translation  of  freely-moving 
molecules.  There  is,  however,  an  important 
limitation,  because  no  gas  absolutely  obeys 
the  mathematical  conception  of  a  gas,  or, 
in  other  words,  actual  gases  depart  under 
some  conditions  widely,  under  other  con- 
ditions extremely  slightly,  from  the  ideal 
gas.  The  molecules  of  an  ideal  gas  are  points 
occupying  no  volume,  and  neither  tractate 
nor  pellate  when  the  gas  contracts  or  ex- 
pands, that  is  to  say  they  are  really  free- 
flying  and  independent.  Hydrogen  and 
helium  under  orclinary  conditions  approach 
so  nearly  the  condition  of  ideal  gases  that 
scarcely  any  error  is  involved  in  their  use  as 
thermometric  substances.  The  helium  or 
hydrogen  constant  volume  gas  thermometer, 
in  which  the  pressure  of  the  gas  is  used  to 
measure  the  temperature  is  the  standard  to 
which  all  others  are  referred.  These  are  the 
two  last  gases  to  liquefy  when  temperature 
is  reduced.  Their  readings  agree  with  one 
another  to -210°  C.,  that  is  to  within  63°  C. 


122  MATTER  AND  ENERGY 

of  the  absolute  zero.  Below  this  there  is  only 
one  thermometric  substance,  helium,  avail- 
able, so  that  there  is  no  check  upon  the  tem- 
peratures it  records.  But  there  is  every 
reason  to  believe  that  under  proper  condi- 
tions the  helium  thermometer  still  registers 
correctly  to  within  3°  C.  of  the  absolute 
zero,  the  lowest  temperature  yet  attained 
and  measured  by  its  aid. 

There  is,  however,  another  idea  involved 
in  temperature,  which,  though  not  implied 
in  the  definition  of  the  Absolute  Scale,  is 
implied  in  the  quantitative  aspect  of  the 
Second  Law  of  Thermodynamics.  The 
change  of  temperature  of  a  substance  is  re- 
lated to  the  quantity  of  heat  energy  it  ab- 
sorbs. In  the  simplest  conceivable  case,  if, 
for  a  given  quantity  of  substance,  one  unit 
of  heat  energy  raised  its  temperature  1°,  two 
units  should  raise  it  2°,  and  so  on.  This  in- 
volves the  supposition  that  all  the  heat 
energy  is  employed  to  raise  the  temperature, 
and  that  the  change  of  temperature  is  the 
only  change  produced  by  the  heat  in  the  sub- 
stance. Before  we  can  enter  this  gate  we 
must  previously  have  obtained  a  clear  concep- 
tion of  what  we  mean  by  temperature  and 
the  change  of  temperature  caused  by  adding 
or  withdrawing  heat  energy.  This  we  already 


CHEMICAL  ENERGY  123 

have,  so  that  all  we  need  now  is  to  specify  as 
the  ideal  substance  a  substance  of  the  kind 
described.  For  such  a  substance  all  the  heat 
energy  absorbed  goes  directly  to  increase 
the  kinetic  energy  of  molecular  translation, 
and  none  is.  used  in  any  other  way.  Now 
it  is  a  most  remarkable  fact  that  the  common 
gases,  such  as  hydrogen  and  nitrogen,  which 
are  so  very  nearly  ideal  thermometric  gases 
in  the  former  sense,  nowhere  approximate 
the  ideal  substance  in  the  sense  just  defined. 
The  quantity  of  heat  energy  necessary  to 
raise  the  temperature  of  molecular  propor- 
tions of  such  ideal  substances  1°  (which  would 
be  termed  the  molecular  heat  of  the  sub- 
stance) must  be  the  same  for  all.  It  is  very 
easy  to  calculate  this  molecular  heat  from  the 
kinetic  theory.  It  is  three  calories.  Every 
other  substance,  in  which  some  of  the  heat 
energy  is  not  employed  in  raising  the  tempera- 
ture, requires  more  than  three  calories.  The 
molecular  heat  of  oxygen,  nitrogen,  and  hy- 
drogen at  constant  volume  (where  no  heat 
is  used  to  do  work  expanding  the  gas  against 
the  pressure  of  the  atmosphere)  is,  as  a 
matter  of  fact,  nearly  5.0  calories.  So  that 
for  these  gases  only  about  f  ths  of  the  heat  sup- 
plied goes  to  raise  the  temperature  of  the  gas 
in  the  sense  defined,  the  remaining  f  ths  being 


124  MATTER  AND  ENERGY 

spent  in  effecting  changes  on  the  gases  other 
than  increasing  the  kinetic  energy  of  their 
molecular  translations.  What  becomes  of 
this  heat?  The  gases  considered  are  all  alike 
in  possessing  molecules  built  up  out  of  two 
atoms.  If  gases  with  more  complex  mole- 
cules are  examined,  like  carbon  dioxide  with 
3  atoms,  ammonia  with  4  atoms,  and  so  on, 
it  is  found  that  the  molecular  heat  steadily 
increases.  As  more  and  more  atoms  are 
contained  in  the  single  molecule,  less  and  less 
of  the  heat  goes  to  raise  the  temperature  and 
more  and  more  is  used  up  in  these  other 
changes,  until  for  complex  gases,  like  benzene 
vapour  containing  12  atoms  to  the  molecule, 
the  heat  used  to  raise  the  temperature  is 
only  between  fth  and  ^th  of  that  not  so  used. 
On  the  other  hand,  gases  containing  only 
one  atom  to  the  molecule,  the  monatomic 
gases,  are  ideal  substances  in  the  sense  just 
used.  Their  molecular  heat  is  always  three 
calories  exactly  as  calculated.  Before  1905 
only  one  monatomic  gas  was  known,  namely, 
the  vapour  of  mercury.  But  the  inert  gases 
present  in  the  atmosphere  discovered  in 
1905,  of  which  argon  and  helium  are  the  best 
known,  are  all  ideal  substances  with  a  molecu- 
lar heat  of  three  calories  as  nearly  as  can 
be  ascertained.  Helium,  as  already  noted, 


CHEMICAL  ENERGY  125 

shares  with  hydrogen  the  distinction  of  being 
an  almost  ideal  substance  for  gas  thermom- 
eters. Yet  with  helium  all  the  heat  energy, 
whilst  with  hydrogen  only  about  fths,  goes 
to  increase  the  kinetic  energy  of  molecular 
translation. 

Monatomic  molecules  alone  retain  all  the 
heat  they  receive  as  "sensible"  heat,  i.e. 
heat  sensible  to  the  thermometer.  The 
greater  the  number  of  atoms  in  the  molecule 
of  a  gas  (which  may  be  very  nearly  a  perfect 
gas  in  the  usual  mathematical  sense)  the 
greater  the  proportion  of  heat  used  up,  not 
in  increasing  the  velocity  of  the  molecule  as 
a  unit,  but  in  other  ways.  A  single  atom  of 
matter  if  it  moves  at  all  moves  as  a  whole, 
and  its  energy  is  kinetic  energy  of  trans- 
lation. A  complex  structure  of  atoms,  in 
addition  to  moving  as  a  whole,  may  possess 
internal  motion  of  the  individual  atoms 
with  reference  to  one  another.  A  colloquial 
way  of  describing  these  various  kinds  of  heat 
energy  is  by  the  terms  path-heat,  spin-heat, 
and  wobble-heat.  In  the  first  the  molecule 
moves  as  a  whole,  in  the  second  it  spins  or 
rotates  as  a  whole,  and  in  the  third  its  parts 
or  atoms  move  with  reference  to  one  another. 

Now  when  a  complex  gas  is  heated  and 
cooled,  the  heat  it  absorbed  in  the  first  process 


126  MATTER  AND  ENERGY 

is  given  up  again  in  the  second.  Therefore 
all  these  various  kinds  of  motion  of  the  mole- 
cule cannot  be  independent.  There  must  be 
continual  readjustments,  as  the  tempera- 
ture is  rising  and  falling,  between  the  path- 
energy,  spin-energy,  and  wobble-energy.  In 
general,  for  any  mean  kinetic  energy  of  trans- 
lation the  molecule  must  possess  a  definite 
kinetic  energy  not  of  translation.  In  this 
difficult  field  the  mathematicians  have  not 
been  afraid  to  apply  their  analysis,  and  the 
law  of  the  equipartition  of  energy  has  been 
extended  to  include  equipartition,  not  only 
as  between  molecule  and  molecule,  but  as 
between  the  various  kinds  of  motion  possible, 
or  degrees  of  freedom  as  the  technical  term 
is,  for  the  same  molecule.  The  similarity  of 
helium  and  hydrogen  in  their  thermometric 
behaviour,  which  at  first  sight  might  not 
appear  very  remarkable,  in  reality  depends 
upon  some  of  the  most  profound  and  far- 
reaching  generalisations  of  mathematical 
physics. 

Recapitulating,  heat  energy  communicated 
to  a  material  substance  increases  the  kinetic 
energy  of  translation  of  the  molecules  as  a 
whole,  and  it  is  only  this  portion  of  the  heat 
energy  which  influences  the  temperature. 
Temperature,  therefore,  is  a  measure  of  one 


CHEMICAL  ENERGY  127 

kind  only  of  heat  energy.  In  addition,  heat 
produces,  in  all  substances  except  the  mon- 
atomic  gases,  many  other  kinds  of  motion, 
to  an  extent  greatly  dependent  upon  the 
nature  of  the  particular  substance.  These 
motions  increase  with  rise  of  temperature  and 
decrease  with  fall  of  temperature,  without 
producing  any  permanent  material  change  of 
the  substance,  but  they  are  altogether  dis- 
tinct from  changes  of  temperature.  They  are 
connected  with  temperature  changes  in- 
directly, because  of  the  universality  of  the 
law  of  equipartition  of  energy,  which  holds 
not  only  as  between  all  freely  moving  par- 
ticles whatever  their  mass,  colliding  among 
themselves,  but  also  as  between  the  various 
kinds  of  motion  in  space  which  these  par- 
ticles can  execute.  The  quantitative  aspect 
of  the  Second  Law  shows  that  none  of  these 
other  kinds  of  heat  energy  ever  can  be  con- 
verted into  other  forms  without  first  coming 
into  evidence  as  sensible  heat,  or  the  kinetic 
energy  of  molecular  translation. 

Obviously  there  is  a  limit  to  the  amount  of 
heat  a  complex  molecule  can  absorb  without 
being  chemically  decomposed  into  more 
simple  molecules.  A  fly-wheel  or  grindstone 
driven  at  too  high  a  speed  bursts  into  pieces. 
A  complex  molecule  similarly  is  dissociated. 


1?,8  MATTER  AND  ENERGY 

It  is  customary  to  distinguish  between  two 
kinds  of  material  changes,  such  as  are  pro- 
duced by  heat.  In  the  first  class,  represented 
by  the  vaporisation  of  a  liquid  or  melting 
of  a  solid,  the  matter  returns  completely  to 
its  initial  state  when  cooled,  and  these  were 
called  physical  changes.  Whilst  in  the  other 
class,  chemical  reactions  are  brought  about, 
new  molecules  are  produced,  and  these  may 
or  may  not  revert  to  their  pristine  condition 
on  cooling.  But  although  at  the  extremes 
the  distinction  between  the  two  classes  of 
change  is  well  marked  there  is  no  definite 
boundary  line.  If  the  heating  of  water  is 
continued,  after  it  has  all  passed  into  steam, 
up  to  high  temperature,  part  of  the  water  is 
decomposed  into  its  constituent  elements, 
hydrogen  and  oxygen.  These  two  gases  may 
be  readily  separated  at  high  temperature 
and  cooled.  Kinetic  energy  of  heat  has  been 
absorbed  and  converted  into  a  new  kind  of 
potential  energy,  the  energy  associated  with 
chemical  change.  Hydrogen  and  oxygen 
molecules,  separate  from  one  another,  but 
intermingling  as  one  gas,  tractate  into  water 
when  the  temperature  is  raised.  Separated, 
they  possess  positional  energy  which,  on  their 
intimate  union  into  the  compound  water, 
passes  into  kinetic  energy,  usually  with  an 


CHEMICAL  ENERGY  129 

explosion  and  the  evolution  of  much  heat. 
The  case  differs  in  degree  only  from  the 
condensation  of  steam  into  water.  Very 
few  of  the  best  known  and  simplest  mole- 
cules withstand  dissociation  into  their  ele- 
ments when  heated  to  1800°  C.,  the  tem- 
perature at  which  the  metal  filament  of  an 
incandescent  lamp  works.  Just  as  no  ex- 
planation is  possible  of  gravitation,  none  can 
be  advanced  of  these  cases  of  physical  and 
chemical  tractation,  unless  we  ascribe  "affin- 
ity" and  "incompatibility"  to  molecules 
and  atoms  as  if  they  were  human.  All 
that  can  be  stated  is  that  it  is  the  nature  of 
hydrogen  and  oxygen  separated  to  tractate 
and  of  explosive  chemical  compounds  to 
pellate.  The  tendency  of  the  time  is  to  refer 
these  actions  ultimately  to  the  interplay 
between  electricity  and  matter,  but  nothing 
very  definite  has  yet  transpired.  Electricity 
as  a  distinct  physical  entity  has  been  recog- 
nised scarcely  more  than  a  decade.  Many 
of  the  commonest  chemical  changes  are 
conditioned  by  the  transport  of  electricity. 
It  is  possible  that  all  cases  of  potential  energy 
involve  the  action  of  electricity  as  well  as  of 
matter. 

The  relations  between  energy  and  matter 
when  the  matter  undergoes  chemical  change 


130  MATTER  AND  ENERGY 

call  for  some  attention.  After  the  extinction 
of  the  first  glimmer  of  light,  with  the  down- 
fall of  the  old  Phlogiston  theory  and  the 
rise  of  the  Lavoisier  school,  chemistry  be- 
came for  a  time  an  almost  purely  material- 
istic science.  It  weighed  everything  that 
gravitated,  analysed  everything  that  was 
found  or  could  be  made,  established  the 
laws  of  chemical  change,  and  founded  the 
architectural  side  of  chemistry — the  part, 
that  is,  which  deals  with  the  precise  manner 
in  which  the  individual  atoms  are  arranged 
within  the  molecule.  But  of  energy  and 
its  importance  in  chemistry  it  understood 
little  until  the  middle  of  last  century.  Now- 
adays, alongside  of  the  material  changes  the 
changes  of  energy  are  studied  as  a  matter 
of  course,  and  new  applications  of  the  laws 
of  thermodynamics  are  being  made,  with 
results  as  valuable  and  as  unsuspected  in 
many  cases  as  those  which  followed  their 
original  application  to  simple  changes  of 
state  such  as  fusion  and  vaporisation.  A 
few  examples  may  suffice  of  some  of  the 
important  developments  of  recent  years. 
In  their  search  for  cheap  energy,  chemists 
have  invaded  even  the  most  out-of-the-way 
places,  and  nothing  is  more  common,  among 
districts  visited  a  few  years  ago  only  by 


CHEMICAL  ENERGY  131 

tourists  in  pursuit  of  the  scenery  of  lakes, 
mountains,  and  waterfalls,  to  find  small 
chemical  factories  dotted  about,  nourished 
by  the  "white  coal,"  as  it  is  termed  abroad, 
the  water  power  before  running  to  picturesque 
waste.  Around  Niagara  Falls  large  towns 
have  sprung  up  connected  with  chemical  in- 
dustries requiring  energy,  whilst  the  valleys 
of  Switzerland  have  been  described  as  "gla- 
cier at  one  end  and  98%  nitric  acid  at  the 
other." 

There  are  two  kinds  of  processes  in  chem- 
istry which  are  with  advantage  carried 
out  in  conjunction  with  the  large  modern 
power  stations.  The  first  are  those  requiring 
exceptionally  high  temperature,  and  the 
second  are  those  requiring  cheap  power. 
For  the  power,  whatever  its  source, — whether 
waterfalls,  natural  gas  or  oil,  waste  gas  from 
blast  furnaces,  or  cheap  coal  at  the  pit's 
mouth, — is  always  first  converted  into  electric 
energy  by  means  either  of  large  turbines  in 
the  case  of  water,  or  of  gas-engines  in  the 
other  cases.  As  electrical  energy,  it  is  trans- 
missible at  high  voltages  cheaply  over  a 
considerable  area,  and  is  readily  and  effi- 
ciently transformed  into  the  particular  kind 
of  electric  energy  most  suited  to  the  process 
served,  or  into  mechanical  energy. 


132          MATTER  AND  ENERGY 

The  first  class  of  process,  requiring  ex- 
ceptionally high  temperature,  is  carried  out 
in  the  electric  furnace,  where  the  current 
passes  either  as  an  arc  within  the  furnace, 
or  through  a  high  resistance,  generating  any 
temperature  up  to  from  3000°  to  3500°  C. 
A  whole  host  of  entirely  new  compounds 
has  thus  been  prepared,  and  many  have 
important  applications.  Calcium  carbide, 
which  gives  acetylene  on  addition  of  water, 
is  a  compound  of  one  atom  of  calcium  and 
two  of  carbon,  obtained  by  so  heating  lime 
and  coke.  Silicon  carbide,  or  carborundum, 
from  sand  and  coke  is  used  largely  as  an 
abrasive  and  polishing  material  in  place 
of  emery.  Moissan  made  his  microscopic 
diamonds  in  the  electric  furnace,  and  nu- 
merous and  unsuccessful  have  been  the  at- 
tempts of  others  to  improve  upon  his  re- 
sults. If  diamonds  were  common  instead 
of  costly,  what  magnificent  tools  could  be 
made  for  certain  purposes  and  how  certain 
industries  like  civil  and  mining  engineering, 
engaged  in  drilling  through  the  solid  rock, 
would  blossom  forth!  This  is  no  idle  dream 
like  the  making  of  gold,  and  the  age  to  suc- 
ceed the  steel  age  in  the  future  may  yet  be  a 
diamond  age.  The  diamond  as  a  gem  is 
beautiful,  but  as  a  tool  it  is  a  power,  on  ac- 


CHEMICAL  ENERGY  133 

count  of  its  magnificent  hardness  and  resist- 
ance to  wear. 

The  second  class  of  industries,  which  is 
concerned  with  substances  requiring  a  large 
amount  of  energy  for  their  production, 
although  not  necessarily  distinct  from  the 
first  class,  have  often  different  objects.  The 
first  class  produce  substances  either  pre- 
viously unknown  or  very  rare,  which  often 
cannot  be  produced  in  any  other  way.  The 
second  produce  well-known  commodities  often 
in  universal  demand  by  new  processes  in 
which  the  energy  is  more  directly  introduced 
than  in  the  old.  For  certain  reasons  the 
element  nitrogen  figures  most  largely  in 
this  class.  The  element  nitrogen  is  one  of 
the  most  interesting  to  chemists  and  one 
of  the  most  important  in  the  processes  of 
life.  It  has  at  first  sight  a  paradoxical 
nature.  Except  for  the  monatomic  gases 
of  the  atmosphere,  it  is  the  most  inert  ele- 
ment known,  entering  into  combination 
with  other  elements  very  reluctantly,  and 
yet  forming  a  very  large  number  of  com- 
pounds, such  as  ammonia,  nitric  acid,  and 
their  salts,  which  are  in  universal  demand. 
Free  nitrogen  from  the  atmosphere  is  to  be 
had  for  nothing  in  unlimited  amount,  but 
combined  nitrogen,  as  in  the  ammonium 


134  MATTER  AND  ENERGY 

salts  and  nitrates,  commands  a  relatively 
high  price,  and  the  demand  for  it  will  increase 
whilst  the  present  sources  of  supply  must 
ultimately  become  exhausted.  Nitrogen  is 
the  essential  element  in  almost  all  explosive 
compounds.  It  forms  a  numerous  class  of 
unstable  derivates,  which  on  a  slight  dis- 
turbance detonate,  the  element  nitrogen 
being  liberated  in  the  free  state  as  a  gas 
with  sudden  enormous  expansion  of  volume 
and  the  accompanying  destructive  effects. 
Nitrogen  is  peculiar,  probably  because  its 
atoms  naturally  tend  to  combine  with  one 
another,  rather  than  with  other  elements, 
to  form  the  very  stable  diatomic  molecule 
N2.  Hydrogen  and  oxygen  also  form  similar 
molecules,  H2  and  O2,  but  in  a  mixture  of 
these  gases,  a  spark  or  any  local  rise  of 
temperature  is  sufficient  to  bring  about  a 
rearrangement  of  partners,  the  atoms  before 
combined  with  atoms  of  the  same  kind 
then  uniting  with  atoms  of  the  other  kind. 
Single  atoms  of  nitrogen  never  exist  un- 
combined,  even  at  high  temperature,  on 
account  of  their  tendency  to  unite  with  one 
another,  and  so  are  not  known.  But  there 
is  good  reason  to  believe  that  as  much 
energy  is  liberated  when  free  single  atoms 
of  nitrogen  unite  to  form  the  diatomic 


CHEMICAL  ENERGY  135 

molecule  of  nitrogen  as  in  any  other  chemical 
change  known.  Hence,  before  the  worthless 
free  nitrogen  of  the  atmosphere  can  be 
converted  into  the  valuable  combined  nitro- 
gen, so  essential  for  agriculture  and  the 
production  of  all  food-stuffs,  this  energy 
must  be  supplied.  Free  atoms  of  nitrogen 
tractate  with  an  unparalleled  conversion  of 
potential  into  kinetic  energy,  and  before 
the  molecule  of  nitrogen,  consisting  of  two 
atoms  united  together,  can  be  made  to  form 
other  compounds,  such  as  ammonia  and  nitric 
acid,  the  two  atoms  must  be  separated 
again.  In  this  process  the  same  amount  of 
kinetic  energy  disappears  and  is  reconverted 
into  energy  of  position.  The  modern  indus- 
trial development  for  the  utilisation  of 
atmospheric  nitrogen  dates  from  but  a  few 
years  back.  In  principle  no  essential  ad- 
vance has  been  made  upon  Cavendish's 
great  discovery  in  the  eighteenth  century 
that,  when  an  electric  discharge  is  pressed 
through  air,  a  small  part  of  the  oxygen  and 
nitrogen  combine  to  form  nitrous  acid. 
Instead,  however,  of  the  energy  of  a  patient 
attendant  turning  the  handle  of  a  frictional 
electrical  machine,  hour  after  hour,  as  in 
Cavendish's  experiment,  to-day  the  power 
of  hundreds  of  thousands  of  horses,  derived 


136  MATTER  AND  ENERGY 

chiefly  from  the  "white  fuel"  of  the  Nor- 
wegian and  Swiss  hill-sides,  are  ceaselessly 
at  work,  turning  dynamos  which  produce 
powerful  high-tension  arcs  in  the  air,  so 
converting  it  partially  into  nitrous  and 
nitric  acids.  Much  of  the  product  is  neutral- 
ised with  lime,  and  the  calcium  nitrate 
resulting  is  employed  as  a  fertiliser  of  the 
soil  in  agriculture.  It  is  an  interesting 
example  of  a  chemical  industry  in  which  the 
raw  materials  cost  nothing  or  next  to  nothing, 
and  all  that  has  to  be  supplied  to  convert 
them  into  products  of  value  is  energy. 
The  conversion  takes  place  in  Nature's  own 
slow  way  in  the  air  and  soil,  but  modern 
civilisation  could  never  subsist  on  this 
parsimonious  allowance.  Energy  it  must 
have  just  in  proportion  as  it  advances,  and 
the  day-to-day  supply  of  sunlight  which 
sufficed  for  the  requirements  of  primitive 
agriculture  is  insufficient  for  modern  inten- 
sive methods. 

It  is  interesting  to  trace  the  source  of  the 
supply  of  combined  nitrogen  on  which  old- 
time  agriculture  depended.  First,  a  very 
slow  oxidation  of  the  nitrogen  in  the  air 
takes  place  whereby  about  11  Ib.  of  com- 
bined nitrogen  are  formed  per  year  per  acre 
of  ground  and  carried  down  by  rain.  It 


CHEMICAL  ENERGY  137 

used  to  be  thought  that  this  process  was 
effected  by  lightning  and  other  discharges  of 
electricity  in  the  atmosphere,  but  this  was 
before  the  days  of  radium.  The  atmosphere 
contains  the  emanation  of  radium,  which, 
though  in  relatively  infinitesimal  amount, 
aggregates  in  the  total  all  over  the  globe  to 
a  very  considerable  quantity,  corresponding 
with  hundreds  of  tons  of  pure  radium.  The 
rays  from  this  radium  emanation  are  very 
effective  in  causing  oxygen  and  nitrogen  to 
combine,  and  no  doubt  the  supply  of  com- 
bined nitrogen  from  the  air  is  largely  due  to 
its  action.  Secondly,  certain  leguminous 
plants,  by  the  aid  of  bacteria  in  nodules  in  the 
roots,  have  the  power  of  converting  atmo- 
spheric nitrogen  into  the  combined  form, 
and  the  empirical  principle  of  the  rotation 
of  crops  depends  on  this  action.  But  other 
bacteria  possess  exactly  the  opposite  power, 
and  undo  the  work  of  the  nitrifying  organ- 
isms. It  is  doubtful  if  this  process  accounts 
very  largely  for  the  maintenance  of  combined 
nitrogen  in  the  soil. 

This  industry  has  another  interest  in  that 
it  is  the  first  in  which  any  uneasiness  has 
manifested  itself  as  regards  the  future.  Some 
years  ago  Sir  William  Crookes,  in  a  Presi- 
dential Address  to  the  British  Association, 


138  MATTER  AND  ENERGY 

drew  attention  to  the  probable  future  failure 
of  the  wheat  supply.  In  addition  to  manure, 
the  only  important  sources  of  combined 
nitrogen  available,  now  that  the  guano 
deposits  are  exhausted,  are  the  natural 
deposits  of  sodium  nitrate  or  Chili  saltpetre 
("caliche")  from  the  rainless  districts  of 
S.  Peru  and  Bolivia  and  the  ammonium 
salts  obtained  as  by-products  in  the  manu- 
facture of  coal-gas.  The  latter  is  largely 
wasted  owing  to  the  extravagant  and  un- 
economical methods  in  vogue  of  utilising 
coal  and  could  be  enormously  improved. 
Both  these  natural  resources,  Chili  saltpetre 
and  coal,  are  far  from  inexhaustible.  The 
former,  it  is  estimated,  will  only  suffice  from 
twenty  to  forty  years  longer  at  the  present 
rate  of  consumption.  The  boisterously  pros- 
perous last  half-century,  in  which  virgin 
territory  was  being  everywhere  opened  up 
and  the  conservation  of  natural  resources 
was  hardly  thought  of,  is  giving  place  to  a 
period  of  reflection  in  which  awkward  inter- 
views between  civilisation  and  its  banker 
are  in  prospect.  The  first  suspicion  that  a 
day  of  reckoning  was  to  follow  arose  out  of 
the  address  of  Sir  William  Crookes,  which 
pointed  out  that  the  wheat  supply  would 
fail  unless  chemists  succeeded  in  solving  the 


CHEMICAL  ENERGY  139 

problem  of  the  fixation  of  atmospheric 
nitrogen.  Note  the  result.  Great  corpora- 
tions have  spent  millions  of  pounds  in  the 
processes  for  utilising  atmospheric  nitrogen. 
The  problem  has  been  practically  solved, 
and  no  doubt  when  the  Chili  saltpetre  supplies 
fail,  or  earlier,  they  will  reap  a  rich  harvest. 
But  how  is  it  done?  Simply  by  the  proper 
expenditure  of  natural  energy,  so  that  the 
question,  as  to  how  long  the  Chili  saltpetre 
beds  will  last,  has  simply  been  merged  into 
the  more  general  problem  of  how  long  the 
natural  resources  of  energy  of  the  globe  will 
hold  out.  In  so  far  as  such  developments 
utilise  the  natural  energy  running  to  waste, 
as  in  water  power,  they  may  be  accounted 
as  pure  gain.  But  in  so  far  as  they  consume 
the  fuel  resources  of  the  globe  they  are  very 
different.  The  one  is  like  spending  the 
interest  on  a  legacy,  and  the  other  is  like 
spending  the  legacy  itself.  The  wheat 
problem,  with  its  uncomfortable  suggestion 
of  impending  starvation  for  a  large  part  of 
the  race,  is  one  particular  aspect  of  a  still 
hardly  recognised  coming  energy  problem, 
which  to  thinking  minds  perplexes  the  whole 
future  and  is  like  "the  cloud  no  bigger  than 
a  man's  hand"  on  an  otherwise  cloudless 
horizon. 


140  MATTEIl  AND  ENERGY 

One  point  remains  before  leaving  the  study 
of  heat  and  chemical  energy.  Why  is  heat 
energy  of  uniform  temperature  the  ultimate 
fate  of  all  energy?  The  power  of  sunlight 
and  coal,  electric  power,  water  power,  winds 
and  tides  do  the  work  of  the  world,  and  in 
the  end  all  unite  to  hasten  the  merry  molec- 
ular dance.  Those  who  have  followed  the 
line  of  thought  that  has  been  pursued  will 
have  little  difficulty  in  answering  this  ques- 
tion. There  is  a  definite  stop  to  the  progress 
of  subdivision  of  matter,  when  the  single  atom 
or  the  single  molecule,  according  as  chemical 
or  physical  methods  of  division  are  employed, 
is  attained.  There  is  a  definite  limit  to  the 
process  of  the  transformation  of  energy, 
when  the  subdivision  and  distribution  of 
that  energy,  both  in  quantity  and  direction, 
among  the  smallest  possible  portions  of 
matter  has  been  achieved.  The  limit  which 
puts  a  stop  to  the  one  process  necessarily 
puts  a  stop  to  the  other.  If  molecules  were 
merely  very  small  particles  of  matter,  rather 
than  the  smallest  possible  single  units, 
and  if  still  smaller  particles  existed,  the  col- 
lision of  two  molecules,  which  for  every 
molecule  in  a  gas  under  ordinary  con- 
ditions takes  place  hundreds  or  thousands 
of  millions  of  times  every  second,  would 


CHEMICAL  ENERGY  141 

result  in  loss  of  kinetic  energy  of  motion 
by  reason  of  the  imperfect  elasticity  of  the 
matter  and  the  subdivision  of  the  part  of 
the  energy  lost  among  these  still  smaller 
particles.  That  is  to  say,  if  molecules  were 
not  a  real  limit  of  subdivision,  molecular 
motion  would  not  be  the  last  stage  in  the 
transformation  of  energy. 

The  definition  that  the  molecules  and 
atoms  are  the  ultimate  limit  of  the  sub- 
division of  matter  by  physical  and  chemical 
agencies  carries  with  it  the  necessary  corol- 
lary that  molecules  and  atoms  must  be 
perfectly  elastic  and  frictionless.  Friction 
and  imperfect  elasticity  are  properties  of 
the  gross  world,  and  express  the  transforma- 
tion of  orderly  motion  into  commotion. 
With  the  molecule  and  the  atom  we  reach 
the  limits  of  subdivision  of  matter.  There 
are  no  smaller  material  particles  among 
which  the  energy  can  be  subdivided,  and 
therefore  we  reach  the  limit  of  subdivision 
of  motion. 

By  following  these  lines  of  inquiry  a  clear 
and  definite  mental  impression  of  the  nature 
of  heat  has  been  gained.  How  external  a 
phenomenon  it  is  to  the  molecular  world. 
Thermal  and  mechanical  energy  are  one 
and  the  same  thing  to  the  individual  mole- 


142  MATTER  AND  ENERGY 

cule.  It  is  true  that  at  sufficiently  high 
temperature  heat  will  bring  about  the  de- 
composition or  dissociation  of  most  complex 
molecules,  and  probably,  if  the  process  were 
pushed  far  enough,  would  resolve  most 
common  gases  into  single  atoms.  But  when 
we  have  reached  this  final  limit  of  sub- 
division we  have  no  reason  to  believe  that 
at  any  temperature,  or  under  any  circum- 
stances, any  of  the  heat  energy  is  transformed 
from  motion  of  the  atom  as  a  whole  into 
internal  commotion.  Were  it  otherwise,  at 
a  sufficiently  high  temperature  the  atoms 
themselves  would  be  dissociated,  and  trans- 
mutation would  take  place  under  the  action 
of  heat.  This  was  the  alchemist's  dream. 
Furnaces  and  crucibles  were  his  main  stock 
in  trade.  Nowadays  by  the  use  of  the  elec- 
tric furnace  we  can  attain  in  a  few  minutes 
temperatures  almost  incomparably  greater 
than  the  utmost  the  alchemist,  after  days 
and  nights  of  anxious  care,  could  attain. 
But  transmutation  does  not  seem  to  lie  that 
way.  Inside  the  atom,  heat  energy  does  not 
exist,  and  temperature  has  no  meaning 
whatever.  Under  transcendental  conditions 
— for  instance,  in  the  sun  and  stars — dis- 
sociation of  the  elements  into  simpler  forms 
has  been  imagined  to  be,  and  may  be  taking 


CHEMICAL  ENERGY  143 

place,  for,  at  these  dazzling  temperatures, 
radiation,  a  phenomenon  which  in  our  study 
of  low  temperature  heat  we  have  not  yet  had 
occasion  to  consider,  is  of  paramount  impor- 
tance, and  radiant  energy  is  very  different  from 
the  energy  of  motion  of  molecules.  However, 
the  fact  remains,  that  so  far,  even  at  the 
highest  attainable  temperature  rendered  avail- 
able by  the  use  of  the  electric  furnace,  no 
indications  of  a  transmutation  of  the  ele- 
ments is  yet  forthcoming. 

Yet  the  atom,  for  all  that,  is  not  Nature's 
unit,  but  ours.  Of  recent  years  radioactivity 
has  been  traced  to  the  spontaneous  disinte- 
gration of  certain  atoms  into  parts  which 
form  lighter  atoms.  The  energy  evolved 
in  this  natural  change  puts  into  the  shade 
every  previously  known  example.  Mass  for 
mass,  the  most  violent  explosives  known, 
in  which  suddenly  the  atoms  composing  the 
molecule  pellate,  liberate  scarcely  a  millionth 
part  of  the  energy  set  free  when  atoms  fly 
to  pieces.  The  great  difference  between  the 
two  cases — between,  that  is,  the  most  fun- 
damental kind  of  material  change  known  ten 
years  ago  and  that  known  to-day — has 
opened  up  for  science  an  entirely  new  horizon. 
Kinetic  energy  only  is  sensible  and  knowable. 
Potential  energy  may  and  does  exist  in  matter 


144  MATTER  AND  ENERGY 

to  an  extent  even  now  scarcely  capable  of 
being  grasped,  but  until  the  matter  changes 
and  its  energy  of  position  is  converted  into 
energy  of  motion,  this  energy  is  unknowable 
and  unavailable. 


CHAPTER  VI 

ELECTRONS   AND   X-RAYS 

To  the  early  philosophers  electricity  was  a 
"fluid,"  weightless  and  immaterial,  it  is  true. 
Concerning  its  real  nature  there  was  pre- 
served a  discreet  silence,  so  that  it  has  been 
remarked  that  any  too  great  curiosity  about  it 
almost  came  to  be  considered  indelicate.  But 
it  was  a  kind  of  fluid,  in  that  it  had  the  power 
of  flowing  through  metals  and  other  conduc- 
tors of  electricity,  much  as  water  flows 
through  a  pipe.  Even  the  best  conductors  of 
electricity  offer  resistance  to  the  flow  of 
electricity,  just  as  the  smoothest  and  widest 
pipes  offer  resistance  to  the  flow  of  water,  and 
some  of  the  electrical  energy  of  the  moving 
electricity  in  the  one  case,  just  as  some  of  the 
mechanical  energy  of  the  flowing  water  in  the 
other,  is,  during  the  passage,  converted  into 
heat.  If  the  wire  through  which  the  current 


ELECTRONS  AND  X-RAYS         145 

flows  is  of  small  cross  section  and  is  made  of 
a  substance  which  is  not  a  particularly  good 
conductor,  such  as  carbon,  then  the  heat 
produced  by  the  friction  to  the  passage  of 
the  electricity  may  heat  it  to  whiteness  and 
cause  it  to  emit  light,  as  in  the  filament  of 
any  electric  lamp.  If  the  mains  actually 
touch  without  any  resistance  to  the  passage 
of  the  current,  a  "short  circuit"  results. 
If  not  protected  the  mains  would  instantly 
melt.  So  to  prevent  this  "fuses"  or  thin 
wires  of  lead  are  introduced  at  suitable 
points,  which  melt  if  the  current  increases 
above  a  prearranged  value,  so  protecting  the 
mains  from  injury.  All  the  applications  of 
electricity  to  incandescent  lighting,  heating, 
and  cooking  depend  on  the  principle  just 
discussed.  There  is  a  generating  station 
from  which  the  electricity  is  pumped  out  into 
one  main  by  a  dynamo.  After  passing 
through  the  lamps  or  heating  apparatus  it 
flows  back  to  the  station  through  a  return 
main,  just  as  water  might  be  pumped  round 
a  system  of  pipes.  The  duty  of  the  staff 
of  the  generating  station  is  simply  to  maintain 
the  pressure  or  head  of  electricity — tech- 
nically called  the  voltage  of  the  supply — 
constant  whatever  quantity  of  electricity  is 
flowing  round.  If  the  demand  increases  more 


146          MATTER  AND  ENERGY 

machines  are  started  and  put  into  duty,  for 
whatever  the  demand  the  pressure  at  which 
the  currents  is  supplied  must  not  vary.  By 
making  the  mains  of  copper  of  the  highest 
possible  conductivity  and  of  sufficient  cross 
sectional  area,  so  that  in  them  the  resistance 
losses  are  small,  and  the  filaments  of  the 
lamps  or  wires  of  the  heating  apparatus  of 
just  the  right  length  and  cross  section  to  let 
the  amount  of  electricity  pass  at  the  prevail- 
ing pressure  or  voltage  to  do  the  work  re- 
quired, by  far  the  greatest  part  of  the  electric 
energy  supplied  is  converted  into  heat  or 
light  at  the  place  wanted,  and  only  a  small 
part  is  dissipated  en  route.  The  Board  of 
Trade  unit  at  which  electric  energy  is  retailed 
to  consumers  in  this  country  is  the  "kilowatt- 
hour" — that  is,  a  thousand  "watts"  acting 
for  one  hour.  The  unit  of  pressure  is  the 
volt,  and  the  unit  of  current  is  the  ampere. 
The  product  of  the  volts  and  the  amperes 
expresses  the  power  in  watts,  and  the  product 
of  this  again  into  the  time  the  current  flows 
the  amount  of  electric  energy  consumed. 
The  heat  equivalent  of  the  watt  is  0.24 
calories.  One  Board  of  Trade  unit  of  elec- 
trical energy  if  converted  into  heat  will 
raise  15.2  pints,  or  nearly  2  gallons  of  water 
from  the  freezing  to  the  boiling-point.  The 


ELECTRONS  AND  X-RAYS         147 

carbon  filament  incandescent  lamp  requires 
about  3|  watts,  whereas  the  new  metal  fila- 
ment lamps  require  only  about  1  watt,  per 
candle-power  of  light  given. 

In  this  country,  electricity  is  almost  al- 
ways generated  from  coal,  and  the  chemical 
energy  of  this  is  first  converted  into  heat  of 
only  moderately  high  temperature,  generally 
in  steam  boilers,  before  it  is  converted  into 
electrical  energy.  Since  this  must  be,  by 
the  laws  of  thermodynamics,  a  wasteful 
process  in  which  the  greater  part  of  the 
whole  heat  energy  goes  down  the  drain,  in 
the  form  of  low  temperature  heat  with  the 
condenser  water  from  the  steam  engine,  it 
follows  that  only  a  small  part  of  the  original 
energy  of  the  coal  finds  its  way  to  consumers' 
houses  as  electrical  energy.  The  conversion 
of  this  into  heat  by  use  is  complete,  a  given 
consumption  of  electric  energy  giving  in  the 
end  a  definite  amount  of  heat,  however  it  is 
employed.  For  this  reason  electric  heating 
must  always  be  costly  as  compared  with 
direct  heating  by  coal.  In  electric  lighting 
the  amount  of  energy  converted  first  into 
light  is  very  small  compared  with  that  con- 
verted directly  into  heat,  and  considerable 
improvement  in  the  efficiency  is  possible  in 
this  direction.  The  part  converted  into 


148          MATTER  AND  ENERGY 

light,  or  radiation,  increases  very  rapidly 
as  the  temperature  of  the  filament  of  the  lamp 
is  raised,  the  light  at  the  same  time  becoming 
more  nearly  white.  The  modern  metal  fila- 
ment lamps,  made  out  of  the  rare  metals 
osmium,  tantalum,  and  tungsten,  run  at  a 
temperature  some  hundreds  of  degrees  hotter 
than  the  older  carbon  filament,  and  their 
increased  efficiency  and  the  whiter  character 
of  their  light  are  due  to  this  higher  tempera- 
ture. But  in  electric  heating  and  cooking  no 
improvements  in  the  efficiency  are  possible. 
All  that  can  be  done  is  to  generate  the  heat 
just  where  it  is  wanted  and  to  prevent  it 
from  getting  out  and  being  wasted  as  much  as 
possible. 

The  simple  idea  of  an  immaterial  fluid 
capable  of  being  pumped  under  pressure 
through  a  metal  wire,  like  water  through  a 
pipe,  suffices,  without  any  deeper  analysis, 
to  explain  in  a  way  some  of  the  most  everyday 
applications  of  the  electric  current.  There  is, 
however,  one  point  which  is  not  covered. 
We  can  tell  which  way  the  material  water  is 
flowing  in  a  stream  by  mere  inspection,  but 
we  cannot  tell  which  way  the  immaterial 
electricity  is  flowing.  It  is  true  we  label  one 
main  as  the  positive  and  the  other  as  the 
negative  for  the  sake  of  distinguishing  them, 


ELECTRONS  AND  X-RAYS        149 

and  there  are  certain  easily  distinguished 
differences  between  the  +  and  —  wires. 
For  example,  when  immersed  in  slightly 
acidulated  water,  hydrogen  is  evolved  at 
the  negative  and  oxygen  at  the  positive 
wire  by  decomposition  of  the  water;  and 
since  the  volume  of  the  hydrogen  is  twice  that 
of  the  oxygen,  and  since  unless  the  wire  is  of  a 
"noble"  metal,  like  platinum,  most  of  the 
oxygen  at  first  liberated  combines  with  the 
metal  forming  an  oxide,  hardly  any  escaping 
as  gas  at  all,  no  other  indication  is  necessary 
to  distinguish  between  the  +  and  — .  But 
does  what  we  call  electricity  flow  from  the  + 
to  the  —  or  vice  versa  ?  We  need  to  go  a  good 
deal  deeper  to  answer  this  question. 

Two  rival  views  held  the  field  with  the 
older  philosophers,  whose  ideas  originated 
in  observing,  not  currents  of  electricity,  but 
stationary  electric  charges.  Some  substances, 
like  glass  rubbed  with  silk  rubbers,  became 
electrified  with  one  kind,  positive  as  they 
conventionally  termed  it;  others,  like  vul- 
canite rubbed  with  flannel  or  cloth,  became 
electrified  with  the  opposite  kind  of  elec- 
tricity, which  was  termed  negative.  Similar 
charges  were  stated  to  "repel"  one  another, 
whereas  opposite  charges  "attract"  one 
another.  Some  supposed  that  there  was 


150  MATTER  AND  ENERGY 

but  one  electric  fluid,  which  was  a  universal 
constituent  of  all  matter,  whether  electrified 
or  not,  the  state  of  positive  electrification 
being  when  the  matter  possessed  either  less 
or  more  than  the  normal  amount,  the  state 
of  negative  electrification  being  the  reverse. 
Others  supposed  that  two  kinds  of  electricity 
existed,  which  were  the  exact  opposite  coun- 
terparts of  one  another,  something  analo- 
gous, possibly,  to  an  object  and  its  mirror 
image.  All  electrical  phenomena  can  be 
explained  as  well  on  the  one  fluid  as  on  the 
two  fluid  idea,  but  our  ignorance  at  the  pres- 
ent time  as  to  whether  there  are  two  kinds  of 
electricity  or  one  is  fundamental.  Until  the 
question  is  settled,  the  hopes  that  have  been 
entertained  that,  through  the  study  of 
electricity,  we  shall  be  able  to  arrive  at  a 
philosophical  explanation  of  matter,  are 
likely  to  prove  unfounded. 

Now,  what  is  the  revolution  of  ideas  which 
the  closing  decade  of  last  century  witnessed? 
The  material  fluid,  water,  to  the  eye  of  the 
poet,  the  symbol  of  peace  and  rest,  its  flow  a 
quiet,  continuous,  gliding  movement,  viewed 
through  the  molecular  spectacles  of  science 
presents  a  picture,  compared  with  which  the 
most  frenzied  struggles  of  a  fighting  mob 
is  almost  absolute  stillness.  So  the  electric 


ELECTRONS  AND  X-RAYS        151 

fluid,  when  it  is  forced  into  the  limelight  of 
searching  inquiry,  undergoes  a  similar  trans- 
formation. No  more  than  matter  does  it 
occupy  space  continuously.  It  consists  of 
a  myriad  of  separate  small  units  or  atoms 
each  leading  an  independent  existence,  like 
individuals  fighting  for  their  own  hands. 
Whereas,  however,  we  know  over  eighty 
different  kinds  of  material  atoms,  we  know 
only  one  atom  of  electricity;  and  this  is  the 
kind  of  electricity  which  is,  by  convention, 
termed  negative  electricity.  If  there  is  only 
one  kind  of  electricity,  and  only  one  so  far  has 
been  isolated  from  matter,  it  is  of  the  kind 
which,  unfortunately,  came  to  be  termed 
negative.  The  atom  of  negative  electricity, 
which  like  the  atoms  of  any  one  element  are 
all  precisely  of  the  same  kind,  and  so  far  as  is 
known  are  not  divisible  into  smaller  units, 
is  termed  the  electron.  The  electron  is  the 
smallest  entity  known  to  science.  Just  as 
the  material  fluids,  liquids  and  gases,  are 
made  up  of  a  vast  swarm  of  minute  particles, 
so  the  electric  fluid,  the  flow  of  which  in  a 
conductor  produces  the  electric  current,  is 
made  up  of  a  vast  swarm  of  separate  electrons. 
The  current  through  a  wire  may  be  likened  to 
the  passage  of  these  negative  electrons,  which 
are  known,  from  the  negative  pole  to  the 


152  MATTER  AND  ENERGY 

positive  pole,  or  in  the  opposite  direction  to 
that  conventionally  assumed.  If  positive 
electrons  also  exist,  and  take  part  in  the  flow 
of  the  current,  these  would,  of  course,  move  in 
the  opposite  direction.  But  so  far  the  positive 
electron,  though  much  sought  after,  has 
eluded  pursuit;  and  however  necessary  it 
may  be  for  the  electrical  theory  of  the  nature 
of  matter,  for  all  purely  electric  and  electro- 
magnetic phenomena,  as  already  remarked, 
one  kind  of  electron  explains  the  known 
facts  as  well  as,  or  possibly  better  than,  two. 
For  mere  purposes  of  description  it  is  briefer 
to  assume  the  existence  of  both  kinds. 

The  electron  was  first  recognized  as  a  sepa- 
rate entity  only  after  it  was  isolated  from 
matter.  Just  as  a  charged  piece  of  sealing 
wax  "attracts"  a  piece  of  paper  or  other 
light  object,  so  a  free  electron  by  virtue  of 
its  being  an  electric  charge  "attracts"  a 
molecule  and  attaches  itself  to  it  when  it 
gets  the  opportunity,  forming  a  negatively 
charged  molecule  or  ion.  The  positive  ion  is 
always  molecular  in  size,  and  is  usually  re- 
garded as  an  electrically  neutral  molecule 
which  has  lost  one  or  more  of  its  normal 
number  of  electrons.  But  the  negative  ion, 
if  produced  in  the  absence  of  all  molecules, 
in  an  almost  perfect  vacuum,  for  example,  is 


ELECTRONS  AND  X-RAYS        153 

not  of  molecular  size,  but  an  entity  2000 
times  lighter  than  the  smallest  known  atom, 
the  atom  of  hydrogen. 

The  term  ion  was  introduced  by  Faraday 
to  explain  the  facts  of  electrolysis,  or  the 
chemical  phenomena  which  occur  when  the 
electric  current  is  passed  through  a  solution, 
usually  in  water,  of  a  compound  substance. 
The  current  was  regarded  as  being  carried 
through  the  liquid  by  the  movement  of 
molecules  charged  with  electricity.  The 
positively  charged  ions  moved  to  the  negative 
pole  and  there  gave  up  their  charges,  the 
molecules  being  deposited,  whilst  the  nega- 
tively charged  ions  moved  to  the  positive 
pole  and  likewise  gave  up  their  charges, 
their  molecules  being  similarly  set  free. 
The  flow  of  the  negative  charges  in  the  one 
and  of  the  positive  charges  in  the  other 
direction  constitutes  the  electric  current. 
Water  itself  is  not  a  good  conductor,  but 
solutions  of  common  metallic  compounds 
usually  conduct,  the  dissolved  substance 
becoming  decomposed,  the  metal  being  de- 
posited in  the  form  of  an  adhering  film  on 
the  negative  electrode,  or  pole,  by  which 
the  current  is  conveyed  to  the  liquid.  This 
is  the  basis  of  all  the  arts  of  electroplating 
with  gold,  silver,  nickel,  copper,  etc.  Now 


154  MATTER  AND  ENERGY 

Faraday  found  that,  comparing  two  metals 
like  copper  and  zinc,  the  atomic  weights  of 
which  are  63.6  and  65.3,  the  current  that 
would  deposit  65.3  grams  of  'zinc  in  one 
solution,  say  of  zinc  sulphate,  would  deposit 
63.6  grams  of  copper  in  another  solution, 
say,  of  copper  sulphate;  whereas  for  silver, 
the  atomic  weight  of  which  is  108,  the  same 
current  led  through  a  silver  sulphate  solution 
would  deposit,  not  108  grams  of  silver,  but 
exactly  twice  this  amount.  Now  silver  is 
a  monovalent  metal  and  can  combine  with 
only  one  atom  of  another  monovalent  element 
like  chlorine,  whereas  copper  and  zinc  are, 
in  the  compounds  stated,  divalent  and  will 
combine  with  two  atoms  of  chlorine.  An- 
other series  of  copper  compounds  is  known, 
however,  in  which  the  copper  is  monovalent, 
like  silver,  and,  if  these  are  electrolysed, 
twice  as  much  copper  is  deposited  from 
them  as  by  the  same  current  flowing  through 
solutions  of  the  commoner  series  of  copper 
salts.  On  the  atomic  theory  of  electricity 
how  simple  these  phenomena  appear,  and 
yet  how  long  was  it  before  the  explanation 
was  applied!  Faraday's  ions  are  compounds 
of  the  atom  or  groups  of  atoms  with  an  atom 
of  negative  or  positive  electricity,  or  an 
electron  less  or  more  than  the  normal  number, 


ELECTRONS  AND  X-RAYS         155 

in  the  case  of  the  monovalent  ions,  with 
two  electrons  in  the  case  of  the  divalent 
ions,  with  three  in  the  case  of  the  trivalent 
ions,  and  so  on.  To  liberate  an  atomic 
weight  in  grams  of  a  metal  requires  that 
just  as  many  electrons  should  be  sent  through 
the  solution,  as  electric  current,  as  there  are 
atoms  in  this  quantity  in  the  case  of  a 
monovalent  metal.  For  divalent  metals 
twice  as  many  electrons  are  necessary,  and 
so  on,  each  material  atom  transporting  one, 
two  or  more  electrons,  but  never  fractions  of 
the  electron.  But  until  the  electron  was 
isolated  from  matter  nobody  had  the  courage 
to  believe  in  it  as  a  separate  entity.  New 
experimental  methods  had  first  to  be  per- 
fected for  obtaining  space  free  from  matter, 
or  in  other  words  a  perfect  or  almost  perfect 
vacuum. 

Toricelli's  famous  experiment  of  filling  a 
glass  tube  completely  with  mercury  and 
inverting  it  in  a  bowl  of  mercury,  whereupon 
the  mercury  fell  in  the  tube  to  the  baro- 
metric height,  about  30  inches  at  sea  level, — 
leaving  a  perfect  or  almost  perfect  vacuous 
space  at  the  top  of  the  tube,  has  been  adopted 
in  the  modern  mercury  pump  as  an  almost 
perfect  means  of  removing  the  air  from  a 
closed  vessel.  When  the  electric  current  is 


156  MATTER  AND  ENERGY 

forced  through  the  gas  in  such  a  vessel, 
connected  with  the  air  pump,  while  the  air 
is  being  gradually  removed,  an  extraordinary 
sequence  of  beautiful  phenomena  present 
themselves.  At  first,  before  the  exhaustion 
commences,  it  requires  an  electrical  pressure 
of  tens  or  hundreds  of  thousands  of  volts 
to  cause  the  current  to  flow  at  all,  and  then 
it  does  so  like  lightning,  as  a  disruptive 
spark  making  a  sharp  noise.  But  as  the  air 
is  pumped  out  the  current  passes  with  much 
greater  facility,  and  requires  only  a  few 
thousand  volts.  The  spark  gives  place  to 
the  glow  of  the  vacuum  tube,  and  the  dis- 
charge broadens  out  until  it  gradually  fills 
the  whole  vessel  completely.  At  this  stage 
the  current  is  carried  by  positive  and  nega- 
tive ions,  or  charged  molecules  of  the  gas, 
streaming  in  opposite  directions  to  the  two 
electrodes,  their  collisions  with  one  another 
probably  causing  the  light.  A  closer  exam- 
ination at  this  stage  will  reveal  the  fact  that 
the  main  resistance  to  the  passage  of  the 
current  is  at  the  boundary  of  the  negative 
electrode  and  the  gas.  That  is  to  say,  the 
electrons  flowing  in  the  metallic  part  of  the 
circuit  from  negative  to  positive,  leave  the 
metal  and  jump  off  into  the  gas  only  with 
great  reluctance,  the  resistance  everywhere 


ELECTRONS  AND  X-RAYS         157 

else  in  the  circuit  to  the  passage  of  the  current 
being  relatively  small.  A  mercury  surface 
in  a  good  vacuum,  although  it  opposes  this 
jumping  off  of  the  electrons  as  much  as  the 
other  metals  do  at  first,  has  the  peculiarity 
that  at  the  moment  the  current  starts  the 
reluctance  practically  disappears.  Once 
started,  the  current,  even  although  at  quite 
low  voltage,  continues  to  flow  through  the 
mercury  vapour  with  ease.  This  is  the 
principle  of  the  mercury  lamp,  which  will 
run  on  the  ordinary  electric  mains.  It  is 
started  by  tilting  the  lamp,  so  that  for  a 
brief  moment  the  mercury  flows  from  one 
pole  across  to  the  other,  causing  a  discharge 
to  pass;  and,  when  once  so  started,  the 
current  will  continue  through  the  mercury 
vapour,  producing  the  well-known  ghastly 
coloured  but  cheap  and  otherwise  pleasant 
light.  Other  means  of  overcoming  this  great 
reluctance  of  the  electrons  to  leave  the  metal 
and  to  enter  the  vacuum  (which  is  known 
technically  as  the  cathode  fall  of  potential) 
are  known.  For  example,  the  effect  may 
be  achieved  by  covering  the  negative  pole 
with  lime  and  making  it  white  hot  (the 
"Wehnelt  cathode").  It  is  not  difficult  to 
predict  that  probably  the  electric  lamp  of 
the  future  will  be  some  form  of  vacuum  tube 


158  MATTER  AND  ENERGY 

capable  of  being  run  from  the  ordinary 
electric  mains.  The  beauty  and  brilliance 
of  the  vacuum  tube  discharge  through  gases 
when  powerful  currents  from  the  mains  at 
low  voltage  are  used,  instead  of  the  very 
small  currents  at  high  voltage  furnished  by 
the  induction  coil,  can  only  be  appreciated 
after  having  been  seen. 

If  we  continue  our  experiment  we  shall 
find  that  when  all  but  from  about  1/1 000th 
to  l/10,000th  part  of  the  airhasbeen  removed, 
the  current  flows  with  the  minimum  of 
opposition,  and  from  this  point,  as  we  go 
on  exhausting,  the  resistance  to  the  passage 
of  the  current  again  increases  and  goes  on 
increasing  very  rapidly  until,  finally,  the 
most  powerful  appliances  known  quite  fail 
to  force  the  discharge  through.  At  this 
stage  the  smaller  the  distance  between  the 
electrodes  the  more  difficult  it  is  to  force 
the  current  through,  and,  at  a  degree  of 
vacuum  easily  reached  nowadays,  the  dis- 
charge may  prefer  to  leap  across  several 
inches  of  the  air  outside  the  vessel  rather 
than  pass  through  an  inch  distance  of  the 
vacuum  within. 

This  is  the  stage  of  vacuum  from  the  study 
of  which  so  much  that  is  new  and  revolu- 
tionary has  been  gleaned.  It  can  only  be 


ELECTRONS  AND  X-RAYS       159 

attained  by  a  mercury  pump  or  equally 
efficient  modern  methods,  and  this  accounts 
for  the  fact  that  the  older  observers,  with 
mechanical  air  pumps,  were  never  able  quite 
to  obtain  the  most  interesting  stage  of  the 
vacuum.  The  discharge  alters  its  character, 
and  interest  centres  around  the  negative 
electrode,  or  "cathode,"  as  it  is  termed. 
The  positive  electrode  or  "anode"  may 
have  any  position  or  shape  without  any 
longer  affecting  the  character  or  direction  of 
the  discharge.  From  the  cathode  and  at 
right  angles  to  its  surface,  there  issue  now 
the  electrons  or  atoms  of  negative  electricity 
in  the  free  state,  unhampered  by  molecules 
of  matter  and  travelling  alone.  Sometimes, 
if  the  vacuum  has  not  been  pushed  to  its 
extreme  limit,  the  paths  of  these  electrons 
("cathode-rays"  or  "cathode-streams,"  as 
they  were  first  and  are  still  called)  can  be 
faintly  seen,  but  usually  it  is  not  until 
they  impinge  upon  an  obstacle  that  they 
become  evident.  If  a  small  piece  of  platinum 
foil  is  put  into  their  path,  it  can  be  heated 
white  hot  and  may  readily  be  melted.  The 
glass  walls  of  the  vessel,  wherever  they  are 
bombarded  by  these  streams,  fluoresce,  usu- 
ally with  a  beautiful  pale  greenish  glow;  and 
if  an  object  of  definite  geometrical  form,  like 


160  MATTER  AND  ENERGY 

a  cross,  is  arranged  in  the  vessel  so  as  to 
intercept  part  of  the  stream,  it  casts  a  shadow 
of  its  own  form,  the  glass  behind  not  fluores- 
cing  where  it  is  protected  from  the  bombard- 
ment. The  electrons  travel  outward  from 
the  cathode  in  straight  lines,  everywhere, 
as  a  first  approximation,  normal  to  the 
surface  of  the  cathode,  and  so  they  resemble 
"rays,"  and  were,  in  fact,  named  "cathode- 
rays"  before  their  nature  was  elucidated. 
Certain  fluorescent  substances,  particularly 
a  silicate  of  zinc  known  as  willemite,  and  the 
class  of  salts  known  as  the  platinocyanides, 
for  example,  platinocyanide  of  barium,  re- 
spond to  the  cathode-rays  far  more  bril- 
liantly than  glass;  and  these  substances  when 
put  within  the  vacuum  tube  produce  the 
most  beautiful  effects.  Sir  William  Crookes 
examined  these  new  phenomena  exhaustively, 
and,  without  actually  elucidating  their  true 
nature,  he  came  near  enough  to  assert  that 
the  effects  were  produced  by  swarms  of 
material  particles  in  a  new  or  fourth  state, 
not  solid,  liquid,  or  gaseous,  but  something 
ultra-gaseous,  or  radiant.  His  name  "Radi- 
ant Matter"  still  survives  along  with  the 
terms  cathode-rays  and  cathode-streams. 

No  subject  was  a  more  favourite  one  for 
lecture  experiments  and  investigation,  but, 


ELECTRONS  AND  X-RAYS        161 

curiously,  all  who  worked  with  these  highly 
exhausted  vacuum  tubes  until  1905  over- 
looked probably  what  would  be  considered 
from  a  utilitarian  point  of  view  the  most 
extraordinary  phenomenon  of  all.  When 
these  electrons  are  forced  out  of  the  negative 
electrode,  they  rush  away  from  it,  by  the  law 
of  the  pellation  of  similar  electric  charges, 
along  straight  lines  like  rays.  When  they 
strike  a  solid  obstacle,  they  are  converted 
into  X-rays,  or  Rontgen  rays.  The  denser 
the  obstacle,  and  therefore  the  more  suddenly 
the  electrons  are  stopped,  the  more  pene- 
trating and  remarkable  are  the  X-rays  pro- 
duced. The  X-ray  tube  is  simply  a  Crookes' 
tube,  with  an  obstacle  of  the  dense  and 
difficultly  fusible  metal  platinum,  called  the 
anti-cathode.  The  cathode  is  made  concave, 
whereby  the  electrons  it  emits  are  brought 
to  a  focus  in  the  middle  of  the  tube,  at  which 
point  the  anti-cathode  is  placed.  Of  the 
application  of  the  X-rays,  discovered  by 
Rontgen,  and  of  their  power  of  penetrating 
matter  opaque  to  light,  it  is  scarcely  necessary 
to  speak,  nor  of  their  invaluable  aid  in 
surgery  and  diagnosis.  They  enable  the 
physician  actually  to  see  the  denser  parts  of 
the  interior  of  the  body,  and  to  locate 
fractures  and  certain  growths.  In  fact,  they 
furnish  him  with  a  veritable  sixth  sense. 


16<&          MATTER  AND  ENERGY 

What  creatures  of  circumstance  we  are, 
awakening  into  consciousness  in  a  com- 
plicated world,  and  apprehending  the  simple 
only  through  much  less  simple  but  more 
obvious  phenomena.  Obvious  inexplicable 
things  force  entrance  even  into  our  philosophy 
and  silence  inquiry.  Why  is  glass  trans- 
parent and  metal  opaque?  Until  the  X-rays 
were  known,  to  which  metals  are  not  specially 
opaque  nor  glass  specially  transparent,  the 
complicated  peculiarities  of  light,  which 
traverses  some  materials  practically  un- 
absorbed,  and  is  completely  stopped  by  the 
thinnest  films  of  others,  seemed  most  natural 
and  commonplace.  The  recognition  that 
there  was  nothing  absurd  about  a  particular 
sort  of  light  traversing  a  sheet  of  iron  or 
stone,  which  arose  with  the  discovery  of  the 
X-rays,  was  extended  by  the  discovery  of 
the  a-,  £-,  and  7 -rays  of  the  radioactive 
substances,  and  by  the  nearer  study  of  the 
cathode-rays.  The  latter,  although  not 
sufficiently  penetrating  to  escape  from  the 
vacuum  tube,  yet  in  their  general  absorption 
by  matter,  do  not  recognise  the  optical 
qualities  of  opacity  and  transparency,  any 
more  than  do  the  X-rays.  In  the  absorption 
of  these  newer  types  of  radiation  we  have, 
as  a  first  approximation,  the  simplest  conceiv- 


ELECTRONS  AND  X-RAYS         163 

able  law.  The  power  of  penetrating  matter 
varies  enormously  with  the  different  types, 
from  that  of  the  a-rays,  which  are  completely 
absorbed  by  a  sheet  of  writing-paper,  to  that 
of  the  y-rays  of  radium,  only  half  absorbed 
by  half  an  inch  of  solid  lead.  But,  for  all, 
the  quantity  or  mass  of  matter  in  the  path 
of  the  ray  is  what  fixes  the  amount  of  absorp- 
tion, and  considerations  of  the  physical  and 
chemical  nature  of  the  matter  hardly  enter. 
All  substances  absorb  these  new  rays  pro- 
portionally to  their  density  as  a  first  approxi- 
mation, when  sheets  of  the  same  thickness  are 
compared.  The  penetrating  power  of  the 
X-rays  varies  very  much  with  the  degree  of 
vacuum  of  the  X-ray  tube.  If  the  vacuum 
is  poor  or  "low,"  the  rays  are  not  very 
penetrating  or  "soft";  whilst  if  the  vacuum 
is  good  the  rays  are  penetrating  or  "hard." 
But  the  most  penetrating  X-rays  fall  far 
short  of  the  y-rays  in  this  respect,  and  are 
never  able  to  penetrate  more  than  a  very 
small  fraction  of  an  inch  of  lead. 


164  MATTER  AND  ENERGY 

CHAPTER  VII 

INERTIA 

IN  attempting  to  follow  further  the  fore- 
going line  of  thought,  we  are  abruptly  pulled 
up  because,  so  far,  we  have  been  concerned 
merely  to  make  electricity,  like  matter, 
atomic  in  structure,  and  to  make  the  electric 
fluid  nothing  more  than  a  particularly  fine- 
grained sort  of  gas,  without  any  reference  at 
all  to  properties  which  the  electron  has,  and 
which  no  material  particle  possesses.  We 
cannot  proceed  more  than  a  very  little  way 
in  the  study  of  electricity  by  the  use  of  mate- 
rial analogies,  any  more  than  we  could  pursue 
the  study  of  bacteria  if  our  minds  were  able 
to  apprehend  nothing  less  highly  organised 
than  a  man.  The  average  mind  will  follow 
easily  the  advances  of  science  so  long  as  they 
may  be  expressed  in  terms  of  mechanical 
models,  and  by  means  of  mental  pictures  of 
concrete  things.  But  when  we  leave  the 
realm  of  matter,  and  attempt  to  penetrate 
into  that  of  electricity  and  the  ether,  the 
highest  intellect  feels  the  need  of  models 
and  the  impossibility  of  obtaining  even  the 
raw  unfinished  material  out  of  which  to  con- 


INERTIA  165 

struct  them.  It  is  as  if  we  were  in  a  world 
destitute  of  simple  wood  and  brass  and  nails, 
but  elaborately  furnished  with  all  sorts  of 
extremely  complicated  constructions  which 
baffle  our  ingenuity  to  pull  to  pieces.  Our 
most  fundamental  conceptions  are,  like  our- 
selves, material.  The  elaboration  of  them  is 
easy,  but  their  simplification  to  suit  the 
immaterial  world,  whither  we  now  wish  to 
embark,  is  difficult  almost  to  impossibility. 
If  our  minds  habitually  thought  in  terms  of 
electricity  and  magnetism  instead  of  in  terms 
of  matter  and  motion,  what  a  world  would  be 
opened  up! 

We  have  first  to  attempt  to  realise  that 
an  electron  is  an  electric  charge  which,  if 
not  prevented,  pellates  from  other  similar 
electrons  or  negative  electric  charges,  and 
tractates  towards  positive  charges.  The 
intensity  of  the  effect  varies,  like  that  of 
gravitation,  inversely  as  the  square  of  the 
distance.  If  a  collection  of  electrons  is 
brought  near  an  uncharged  mass  of  matter 
of  finite  size,  the  electrons  in  the  matter 
pellate  to  the  further  side,  leaving  the  side 
nearest  to  the  electron  positively  charged 
(by  induction,  as  it  is  called).  The  opposite 
charges  being  nearer  than  the  like  charges, 
the  tractation  overpowers  the  pellation.  Un- 


166  MATTER  AND  ENERGY 

charged  masses  in  the  proximity  of  electric 
charges  of  either  sign  tend  to  approach  these 
charges.  These  effects  are  very  much  greater 
than  any  of  mechanical  origin.  To  fix 
our  ideas  we  must  first  have  in  our  minds 
some  definite  quantity  of  electricity  or  some 
definite  number  of  electrons.  Suppose  we 
take  as  many  electrons  (7X1023)  as  there 
are  atoms  in  a  gram  of  hydrogen  or  in  108 
grams  of  silver.  This  is  the  number  con- 
veyed through  a  circuit  by  a  current  capable 
of  depositing  108  grams  of  silver  from  a 
silver  solution  in  an  electroplating  bath. 
It  is  roughly  the  number  flowing  in  four 
days  through  the  filament  of  a  16  candle 
power  carbon  incandescent  lamp  burning 
on  a  200  volt  circuit,  or  through  an  ordinary 
10  ampere  arc-lamp  in  2  hours  41  minutes. 
If  two  such  quantities  of  electricity  were 
placed,  one  at  the  North  and  the  other  at 
the  South  Pole  of  the  earth,  they  would 
tend  to  pellate  so  strongly  that,  even  at 
this  distance,  a  fairly  thick  steel  cable, 
capable  of  supporting  the  weight  of  35  tons, 
would  be  necessary  to  keep  them  from 
moving  apart.  Since  the  pellation  decreases 
as  the  square  of  the  distance,  if  two  such 
quantities  were  placed  near  together  no 
material  bond  would  hold  them.  The 


INERTIA  167 

obvious  conclusion  since  electrons  have  these 
properties,  is  that  it  would  be  quite  im- 
possible ever  to  keep  the  number  supposed 
in  the  illustration  together  in  one  place, 
for  every  one  would  fly  away  from  every 
other,  bursting  into  fragments  any  material 
obstacle  to  their  motion. 

Hence,  when  we  wish  to  construct  an 
electrical  model,  and  begin  on  the  raw  mate- 
rial, electricity,  we  are  confronted  at  once  with 
a  set  of  conditions  quite  alien  to  anything 
with  which  we  are  familiar.  The  brass  and 
wood  and  nails  of  our  mechanical  models, 
when  collected  together,  remain  where  they 
are  put,  whereas  free  electricity,  if  not 
prevented,  dissipates  its  constituent  particles 
as  far  as  possible  from  one  another.  The 
moral  of  this  illustration  is  that  it  is  impossi- 
ble to  have  many  free  electrons  in  any  mass 
of  matter.  When  a  small  ball  is  charged 
negatively  to  the  highest  possible  point,  so 
that  the  charge  is  leaking  away  from  it  on 
all  sides  through  the  air  in  the  form  of  brush 
discharges,  the  number  of  free  electrons  it 
possesses  is  not  greater  than  one  for  every 
million  million  atoms.  The  charge  we  have 
taken  as  a  unit,  namely,  that  carried  by  one 
gram  of  hydrogen  ions,  would,  if  free, 
charge  the  whole  world  up  to  a  potential  of  a 


168          MATTER  AND  ENERGY 

million  volts.  Free  electricity,  uncombined 
with  matter,  is  wonderfully  potent,  and  in 
the  most  powerful  manifestations  of  it,  the 
actual  quantity  involved  is  very  insignificant. 
Although  very  considerable  numbers  of 
electrons  must  flow  to  produce  even  a  feeble 
current  of  electricity,  the  greatest  charge 
of  stationary  electricity  known  to  us  is  in 
reality  an  exceedingly  small  quantity,  and 
we  can  never  apprehend  free  electricity 
uncombined  with  matter  in  anything  but 
infinitesimal  amounts.  The  key  to  future 
progress,  as  already  remarked,  is  the  an- 
swer to  the  question,  "What  is  positive  elec- 
tricity?" In  other  words,  what  controlling 
agent  is  it  which  neutralises  the  pellation  of 
the  electrons  in  a  piece  of  electrically  neutral 
metal,  and,  but  for  which,  the  contained 
electrons  would  be  explosively  expelled  to  the 
ends  of  space,  carrying  the  metal  with  it,  if 
they  could  not  move  without  it?  If,  in  the 
metal,  there  were  an  equal  number  of  positive 
electrons,  the  two  sets  would  neutralise  one 
another,  but  why  then  is  the  positive  elec- 
tron never  obtained  free?  One  cannot 
but  feel  that  the  answer  to  this  question 
underlies  the  secret  of  the  structure  of 
matter,  and  that  the  expression  positive 
electricity  is  but  a  mere  term  cloaking  total 


INERTIA  169 

ignorance  of  the  essential  character  of  the 
structure  the  electrical  theory  of  matter 
attempts  to  explain. 

The  electron  has  been  spoken  of  as  im- 
material in  the  sense  that  it  is  not  matter, 
but  something  at  once  finer  grained  and 
endowed  with  fundamental  qualities  which 
distinguish  it  from  any  of  the  known  kinds 
of  matter.  But  electric  energy  has  also 
been  spoken  of  as  the  kinetic  energy  of 
moving  electrons.  Kinetic  energy  is  measured 
by  half  the  product  of  the  mass  into  the 
square  of  the  velocity.  Any  moving  particle, 
whether  it  is  material  or  not,  possessing 
kinetic  energy  and  able  to  agitate  the  mole- 
cules of  matter,  or,  what  is  the  same  thing 
differently  expressed,  capable  of  being  con- 
verted into  heat,  must  possess  mass.  A 
massless  particle  would  belong  to  that  other 
world  of  spirits  and  dreams,  the  inhabitants 
of  which  are  not  "conserved,"  and  the 
study  of  which  belongs  not  to  physical 
science.  A  massless  particle,  so  far  as 
can  be  seen,  if  it  in  any  way  acquired  energy, 
however  infinitesimal,  would  move  at  infi- 
nite velocity,  and  would,  therefore,  leave 
the  universe  behind  it  without  the  lapse 
of  time.  Whether  or  not  future  generations 
will  find  any  room  for  massless  particles 


170  MATTER  AND  ENERGY 

in  their  philosophy,  the  present  can  hardly 
conceive  them  to  exist,  or  imagine  how 
they  could  become  known  if  they  did.  It 
is  just  because  the  electron  has  a  definite 
mass,  even  though  it  is  by  far  the  smallest 
of  any  known,  and  still  is  not  a  material 
particle,  that  its  chief  interest  lies.  Assuredly 
science  has  here  penetrated  one  step  farther 
into  the  eternal  verities.  With  many  of 
the  feelings  of  an  airman,  who  has  left 
behind  for  the  first  time  the  solid  ground 
beneath  him,  let  us  try  to  venture  into  this 
new  region  of  science,  of  mass  without 
matter. 

Mass  and  matter  are  to  us  almost  syno- 
nyms. Indeed,  mass  has  been  defined  as 
quantity  of  matter.  True  to  the  fatal  habit 
of  accepting  obvious  things  as  fully  explained 
or  fundamental,  few  will  ever  have  set 
themselves  to  abstract  the  idea  of  mass  from 
matter,  so  that  this  must  first  be  done. 
We  must  first  take  care  not  to  confound 
mass  with  weight  to  which  it  is  proportional 
at  any  one  latitude.  The  law  of  gravitation 
acts  universally  on  matter  endowing  it  with 
weight  due  to  the  tractation  of  the  matter 
towards  the  immense  mass  of  the  earth, 
from  which  we  can  never  get  far  away.  If 
we  could  remove  to  a  place  in  space  remote 


INERTIA  171 

from  worlds  of  all  kinds,  the  weight  of  the 
matter  would  practically  disappear,  but  its 
mass  would  be  unchanged.  Under  such 
conditions  we  should  bring  into  prominence 
the  true  fundamental  attribute  of  matter, 
its  inertia,  or  its  disinclination  to  move 
when  at  rest,  and  its  disinclination  to  stop 
moving  after  it  has  been  started.  Moving 
it  possesses  energy,  the  kinetic  energy  of 
motion.  Before  it  can  start  energy  must 
be  supplied  to  the  matter,  and  before  it  can 
stop  this  energy  must  be  taken  from  it. 
Unless  it  loses  its  energy  it  will  continue  to 
move,  if  moving  originally,  and  its  motion 
will  be  uniform  and  perpetual.  It  seems  the 
most  natural  thing  in  the  world  that  matter 
should  possess  this  inertia,  so  natural  indeed 
that  to  ask  why  might  seem  a  foolish  ques- 
tion. At  least  the  question  was  never  asked 
before  the  electron  was  studied  and  it  was 
found  that  the  inertia  of  an  electron,  the 
property  by  virtue  of  which  a  moving  elec- 
tron possesses  kinetic  energy,  accounted 
also  for  a  great  deal  more  than  its  inertia. 
Electric  currents,  which  we  have  seen 
are  due  to  the  flow  of  electrons,  are  not 
merely  moving  charges  of  electricity.  So 
far,  attention  has  been  confined  practically 
to  the  heating  effects  of  the  current,  or  to  the 


in          MATTER  AND  ENERGY 

communication  of  the  motion  of  the  electrons 
by  friction  or  resistance  to  the  molecules  of 
matter.  A  charge  of  electricity,  or  electrons 
at  rest,  has  no  magnetic  properties.  A 
current  of  electricity,  or  the  same  electrons 
in  motion,  has.  The  electrons  flying  free 
from  matter  in  the  Crookes'  tube  are  turned 
out  of  their  course  when  one  pole  of  a  bar 
magnet  is  brought  near  to  the  tube.  Faraday 
imagined  that  "  lines  of  magnetic  force  "  ex- 
tend out  from  a  magnet  into  space.  These 
lines,  which  we  shall  simply  refer  to  as  the 
magnetic  lines,  merely  point  the  direction 
along  which  magnetised  bodies  tend  to 
approach  a  magnet.  In  the  case  of  a  bar 
magnet  the  lines  continue  out  in  the  direction 
of  the  length  of  the  magnet.  If  a  narrow 
pencil  of  cathode-rays  is  examined,  it  will  be 
found  that  when  the  bar  is  held  so  that  its 
length  is  at  right  angles  to  the  path  of  the 
rays,  the  latter,  when  they  pass  the  end  of 
the  pole,  are  turned  to  one  side  in  a  plane  at 
right  angles  to  the  length  of  the  bar  magnet. 
If  the  other  pole  of  the  magnet  is  then  pre- 
sented, the  rays  will  be  turned  just  as  before, 
but  to  the  other  side.  But  these  same 
electrons  at  rest,  as  a  simple  electric  charge, 
are  not  moved,  nor  affected  in  any  way 
whatever  by  a  stationary  magnet.  It  is  true 


INERTIA  173 

that  they  are  affected  by  a  moving  magnet, 
but  a  magnet  moving  with  reference  to  an 
electron  comes  to  the  same  thing  as  the 
electron  moving  with  reference  to  a  stationary 
magnet.  If  the  two  poles  of  a  magnet  are 
bent  round  so  that  they  are  opposite  each 
other,  the  magnetic  lines  are  in  the  direction 
of  the  shortest  straight  lines  joining  the  two 
poles.  A  cathode-ray  travelling  up  between 
the  poles  at  right  angles  to  the  magnetic 
lines  is,  if  the  magnet  is  strong  enough,  coiled 
into  a  circle  having  one  of  the  magnetic  lines 
as  its  axis.  If  it  is  not  travelling  at  right 
angles  to  the  magnetic  line,  it  pursues  a  spiral 
path  around  the  magnetic  line,  its  component 
of  velocity  along  the  magnetic  line  not  being 
affected.  If  it  is  travelling  in  the  direction 
of  the  magnetic  lines,  its  motion  is  unaffected 
by  the  magnet.  In  the  first  case  referred  to, 
the  electrons  assume  a  new  motion,  the 
direction  of  which  is  at  right  angles  to  the 
magnetic  lines  and  at  right  angles  to  the 
original  path  of  motion  of  the  rays.  We  live 
in  a  world  of  three  dimensions — length, 
breadth,  and  depth.  If  the  direction  of  the 
electron's  original  motion  is  along  the  length, 
and  that  of  the  magnetic  lines  along  the 
breadth,  the  electron  departs  from  its  original 
path  with  a  new  motion  in  the  direction  of 


174  MATTER  AND  ENERGY 

the  depth.  The  diameter  of  the  circle  into 
which  the  path  of  the  ray  is  coiled  depends 
upon  three  things — 

(1)  The  strength  of  the  magnet,  which  is 
easily  measured. 

(2)  The  momentum  of  the  electron — that 
is,  the  product  of  its  velocity  and  its  mass 
or  inertia. 

(3)  The  magnitude  of  the  charge  of  the 
electron. 

Now  the  path  of  a  cathode-ray  is  affected 
also  by  the  presence  of  an  electrically  charged 
object.  Suppose  a  cathode  particle  travels 
horizontally  between  two  horizontal  parallel 
plates,  the  upper  of  which  is  negatively 
charged,  so  that  the  electron  moves  away 
from  it,  and  the  lower  of  which  is  positively 
charged,  so  that  the  electron  moves  towards 
it,  a  new  downward  motion  is  given  to  the 
particle.  The  path  of  the  ray  will  now  be  a 
curved  path,  precisely  similar  to  that  of  a 
bullet  fired  horizontally  from  a  cliff.  In 
both  cases  the  particle  moving  originally  uni- 
formly in  a  horizontal  direction  tends  to  fall 
with  a  uniform  acceleration.  That  is  to  say, 
the  path  will  curve  downward  in  a  parabola, 
and  the  rapidity  with  which  the  particle 
falls  will  again  depend  on  three  things — 

(1)  The  strength  of  the  charges  on  the 


INERTIA  175 

plates  and  their  distance  apart,  which  are 
easily  measured. 

(2)  The  kinetic  energy  of  the  particle — 
that  is,  the  product  of  half  the  mass  into  the 
square  of  the  velocity. 

(3)  The  magnitude  of  the  charge  of  the 
electron. 

From  experiments  of  this  character  Sir 
J.  J.  Thomson  deduced  the  separate  values 
of  the  mass  of  the  electron,  of  its  charge, 
and  of  its  velocity.  He  found  that  the  mass 
was  less  than  l/1000th  of  that  of  the  hydro- 
gen atom.  The  most  recent  determina- 
tions make  it  about  1 /2500th  of  the  mass  of 
the  hydrogen  atom. 

The  velocity  varies  a  good  deal  with  the 
state  of  the  vacuum  in  the  tube  in  which 
the  cathode-ray  is  generated,  but  does  not 
usually  exceed  about  one-fifth  that  of  light 
or  37,000  miles  a  second.  Radium,  on  the 
other  hand,  emits  /3-rays,  which  are  these 
same  electrons  travelling  free,  with  a  velocity 
very  much  greater,  and  some  travel  practi- 
cally with  the  speed  of  light  itself.  The 
diameter  of  the  electron  has  been  also  approxi- 
mately calculated  and  found  to  be  only 
about  l/100,000th  of  that  of  an  average  mole- 
cule, so  that  both  in  mass  or  inertia  and  in 
size  the  electron  is  incomparably  smaller  than 


176          MATTER  AND  ENERGY 

the  smallest  particle  previously  known  to 
science.  Sir  Oliver  Lodge  has  likened  the 
electrons  in  an  atom  to  flies  in  a  vast  cathe- 
dral. From  being  a  rare  phenomenon,  first 
studied  free  in  a  good  vacuum,  the  electron 
has  been  found  to  play  a  large  part  in  the 
most  varied  phenomena,  usually  associated 
with  atoms  of  matter.  The  radioactive 
substances,  however,  as  has  been  mentioned, 
emit  /3-rays,  which  are  nothing  but  cathode- 
rays,  or  free-flying  electrons,  only  travelling 
at  much  higher  velocity.  In  spite  of  these 
extensions  of  our  knowledge,  only  one  kind 
of  electron  is  known,  and  that  is  identical  in 
all  respects  with  that  described. 

Long  before  the  electron  was  known, 
however,  it  had  been  mathematically  pre- 
dicted that  an  electrically  charged  piece  of 
matter  must  have  a  greater  inertia,  and 
therefore,  in  this  sense,  a  greater  mass  than 
the  same  matter  without  the  charge.  But 
if  we  deal  with  visible  charged  objects,  or 
even  with  charged  single  molecules  or  ions, 
the  part  of  the  mass  contributed  by  the 
charge  is  such  a  minute  proportion  of  the 
whole  that  the  prediction  had  only  an 
academical  interest.  With  the  advent  of 
the  electron,  a  particle  probably  100,000 
times  smaller  and  2000  times  lighter  than 


INERTIA  177 

the  smallest  hitherto  recognised,  the  pre- 
diction became  of  supreme  importance.  For 
it  was  recognised  that  the  inertia,  or  mass, 
of  an  electron  might  be  entirely  due  to  the 
perfectly  well-known  electro-magnetic  phe- 
nomena which  take  place  when  an  electric 
charge  is  put  in  motion,  and  the  subsequent 
development  of  the  subject  has  borne  out 
this  idea.  In  this  one  case  we  have  a  sufficient 
philosophical  explanation  of  the  property 
we  call  inertia,  and  at  once  the  question 
arises:  Is  the  unexplained  inertia  of  matter 
a  different  thing  from  the  elucidated  inertia 
of  electricity,  or  is  it  possible  that  the  inertia 
of  matter  is  due  to  the  same  phenomena  as 
that  of  electricity,  and  that  matter  is  in  some 
unknown  way  compounded  entirely  out  of 
electrons? 

We  have  seen  that  a  current  flowing  along 
a  wire  may  be  considered  simply  as  a  collec- 
tion of  electrons  moving  in  the  wire  from  its 
negative  to  its  positive  end.  If  such  a  wire 
is  flexible  enough  it  will  behave  to  a  magnet 
exactly  like  the  pencil  of  cathode-rays  we 
have  just  considered,  and  will  coil  itself 
round  the  magnetic  lines  in  circles  or  spirals. 
If  the  wire  is  coiled  up  into  a  spiral,  or  solen- 
oid, it  becomes  itself  a  magnet  as  soon  and  for 
as  long  as  the  current  flows,  but  if  the  current 


178  MATTER  AND  ENERGY 

is  stopped  the  magnetism  disappears.  The 
magnetism  is  enormously  strengthened,  but 
not  otherwise  changed,  if  a  bar  of  iron  is 
inserted  into  the  coil,  thus  forming  what  is 
known  as  an  electro-magnet.  From  such  a 
solenoid,  with  or  without  its  iron  core,  mag- 
netic lines  extend  from  the  ends  just  as  in  the 
case  of  a  bar  magnet.  The  surrounding  space 
has  been  changed,  in  that  it  has  become 
magnetised  by  the  motion  of  the  electrons 
in  the  wire.  It  is  impossible  without  a  knowl- 
edge of  electro-magnetism  to  go  into  these 
matters  very  deeply,  but  it  will  be  sufficient 
if  we  confine  ourselves  to  one  important 
general  aspect  of  this  change  which  takes 
place  when  the  current  flows  in  the  solenoid 
and  the  surrounding  space  becomes  magnet- 
ised. When  the  current  is  flowing  the  sur- 
rounding space  has  been  endowed  with  energy, 
known  as  electro-magnetic  energy,  which  it 
does  not  possess  when  the  current  does  not 
flow.  So  we  arrive  at  the  philosophical 
explanation  of  the  inertia  of  an  electron. 
The  space  around  an  electron  at  rest  becomes 
endowed  with  energy  when  the  electron 
moves,  and  before  the  electron  can  again  be 
stopped  this  energy  must  be  withdrawn. 
This  we  have  seen  is  what  we  mean  when  we 
speak  of  the  attribute  inertia. 


INERTIA  179 

We  have  seen  that  a  stream  of  electrons 
flowing  at  right  angles  across  a  magnetic 
line  experiences  a  sideways  thrust,  in  a 
direction  at  right  angles  both  to  its  original 
path  and  to  the  magnetic  line  of  force.  In- 
stead of  moving  the  electrons  past  the  magnet, 
we  may  move  the  magnet  past  the  stationary 
electrons,  which  will  experience  a  thrust  just 
as  before,  and  if  free  to  move — if,  for  example, 
they  are  the  electrons  resident  in  a  piece  of 
metal  forming  part  of  a  closed  metal  circuit — 
we  shall  get  a  flow  of  electrons  in  the  metal 
in  the  stated  direction.  That  is  to  say,  we 
may  generate  an  electric  current  by  the 
passage  of  a  wire  through  the  poles  of  a 
magnet.  Imagine  a  straight  copper  wire 
stretched  horizontally,  and  a  magnet  moved 
from  above  vertically  downward  so  that  the 
wire  passes  between  the  poles  cutting  the 
magnetic  lines  between  them.  The  electrons 
in  the  wire  will  be  urged  along  it  as  the 
magnet  passes,  and  if  the  ends  of  the  wire 
are  connected  to  any  circuit,  through  which  a 
current  is  capable  of  flowing,  a  momentary 
current  will  traverse  the  circuit.  The  modern 
dynamo  works  on  this  principle,  and  may  be 
looked  upon  as  an  electron  pump.  The  wire 
is  arranged  to  lie  parallel  to  the  axis  on  the 
surface  of  a  cylinder  spinning  between  the 


180          MATTER  AND  ENERGY 

poles  of  a  magnet,  and  so  in  its  revolution  is 
continually  crossing  and  recrossing  the  mag- 
netic lines.  Usually  a  large  number  of 
copper  wires  wound  in  a  peculiar  way  on  an 
iron  core — the  whole  being  termed  an  arma- 
ture— rotates  between  the  poles  of  a  power- 
ful stationary  electro-magnet.  The  thrusts 
which  the  electrons  in  the  wire  experience 
as  the  wires  cut  the  magnetic  lines  are  usually 
arranged,  by  means  of  a  commutator,  to  act 
all  in  the  same  direction  and  so  all  unite 
to  drive  the  electrons  out  of  one  pole  and 
to  draw  them  in  at  the  other  pole  of  the 
machine.  When  the  outer  circuit  is  open, 
so  that  no  current  flows,  the  power  necessary 
to  drive  the  machine  is  only  that  wasted  in 
friction  of  the  bearings,  etc.  But  when  the 
circuit  is  closed,  so  that  a  certain  current 
flows,  an  added  amount  of  power  is  necessary 
to  force  the  electrons  against  the  resistance 
of  the  circuit.  The  dynamo  transforms  this 
added  mechanical  energy — the  kinetic  energy 
of  moving  matter — nearly  quantitatively  into 
electric  energy — the  kinetic  energy  of  moving 
electrons. 

If  now  with  the  dynamo  at  rest,  but  with 
its  magnet  excited,  we  pass  a  current  through 
the  armature,  the  machine  becomes  an 
electric  motor.  The  electrons  now  urged  by 


INERTIA  181 

outside  energy  through  the  wires  in  the 
magnetic  field  turn  the  wires  and  with  them 
the  armature.  Perfect  reciprocity  is  the 
feature  of  these  mechanical,  electric,  and 
magnetic  actions.  Very  few  mechanical 
engines  are  reversible  in  this  sense.  If  you 
drive  a  steam  engine  you  do  not  raise  steam 
in  the  boiler.  In  the  world  of  electricity  and 
the  ether,  however,  nothing  can  move  in  one 
dimension  of  space  without  attendant  con- 
sequences in  the  other  two  dimensions. 

These  relations  between  the  electron  and 
the  external  field  of  energy  which  attends 
its  motion  are  perfectly  reciprocal.  On  the 
one  hand,  the  electron  cannot  move  from 
rest  without  this  attendant  field  of  energy 
around  it  coming  into  existence,  and  cannot 
be  stopped  without  this  attendant  field  of 
energy  disappearing  from  the  ether.  On  the 
other,  the  creation  of  a  magnetic  field  in 
space  endows,  or  tends  to  endow,  all  the 
electrons  in  that  space  with  motion  in  one 
direction,  and  the  cessation  of  the  magnetic 
field  endows,  or  tends  to  endow,  them  with 
motion  in  the  opposite  direction.  A  steady 
current  of  electricity,  or  flow  of  electrons 
in  a  circuit,  produces  no  change  in  the  sur- 
rounding magnetic  field.  A  steady  magnetic 
field  produces  no  movement  of  electrons 


182          MATTER  AND  ENERGY 

within  it,  and  so  no  electric  current.  Elec- 
trons changing  the  speed  or  direction  of  their 
motion  produce  attendant  changes  in  the 
surrounding  magnetic  field,  and  conversely 
a  change  in  the  direction  or  strength  of  a 
magnetic  field  produces  motion  or  tendency 
to  motion  of  the  contained  electrons.  These 
phenomena,  well  known  since  the  discoveries 
of  Faraday,  who  termed  them  electro-mag- 
netic induction,  now  lie  at  the  very  founda- 
tion of  the  modern  science  of  electrical 
engineering.  They  have  no  mechanical 
analogies,  for  they  belong  to  a  more  funda- 
mental world  than  that  of  matter.  It  has 
been  stated  that  space  has  three  dimensions — 
length,  breadth,  and  depth — rather  than  any 
of  the  other  numbers  which  mathematicians 
have  attempted  to  picture,  because  of  the 
peculiarities  of  the  ether,  in  which  motion 
in  any  direction  is  attended  simultaneously 
by  influences  acting  in  the  two  directions  at 
right  angles  to  it  and  to  each  other.  However 
this  may  be,  until  it  is  possible  to  educate 
the  mind  so  that  it  apprehends  intuitively 
the  three  dimensional  aspects  of  motion  in 
the  ether,  the  electro-magnetic  world,  which 
underlies  the  material  world  and  which  may 
completely  embrace  it,  must  remain  a  foreign 
element  as  difficult  to  breathe  as  air  is  to  a 


RADIATION  183 

fish,  by  those  accustomed  only  to  the  grosser 
ideas  of  matter  and  its  motion.  It  is  a  time 
of  transition.  The  discovery  of  the  electron 
has  to  a  certain  extent  rendered  the  subject 
concrete  and  picturable,  but  the  pioneers 
even  have  hardly  yet  cleared  their  way 
through  the  jungle  of  obsolete  and  confus- 
ing habits  of  thought  which  naturally  still 
surround  the  subject.  Only  a  few  of  the 
more  important  cases  can  here  be  attempted, 
and  the  first  of  these  is  one  of  the  oldest. 


CHAPTER 

RADIATION 

THERE  is  still  a  gap  in  the  chain  of  reason- 
ing to  be  supplied.  When  an  electron  is 
being  urged  on  to  move  from  rest  at  a  con- 
tinually increasing  speed,  surrounding  its 
path  there  is  being  built  up,  as  the  expression 
goes,  a  magnetic  field  of  greater  and  greater 
strength.  The  energy  being  put  into  the 
electron  overcoming  its  inertia  flows  out 
continuously  into  the  space  surrounding  its 
path  and  travels  along  with  it.  When  the 
electron  is  being  retarded  and  brought  to 


184  MATTER  AND  ENERGY 

rest,  the  energy  it,  itself,  is  now  supplying, 
by  virtue  of  its  inertia,  flows  in  from  the 
surrounding  space  and  the  magnetic  field 
gradually  weakens  and  disappears.  As  we 
know  that  the  magnetic  field  extends  for 
a  considerable  distance  all  round  an  electro- 
magnet, these  outgoings  and  incomings  of 
energy,  between  the  electron  and  its  en- 
vironment, involve  the  transference  of  energy 
over  considerable  distances,  and  as  the  air 
or  surrounding  matter  plays  no  part  in  the 
phenomena,  they  must  take  place  through 
empty  space.  It  is  not  too  much  to  say 
that  the  idea  of  an  ether  has  been  invented 
by  scientific  men  for  the  express  purpose  of 
accounting  for  the  flow  of  energy  across 
empty  space,  and  is  at  present  little  more 
than  a  term  to  express  the  medium  in  which 
these  transferences  occur.  Action  at  a  dis- 
tance, be  it  gravitation,  electric  pellation 
or  tractation,  or  magnetic  action,  carries 
with  it  the  necessity  of  supposing  something 
to  exist  in  the  intervening  space,  and  science 
takes  the  simplest  possible  view  when  it 
supposes  that  one  such  universal  medium, 
the  ether,  fills  all  space,  alike  between  the 
molecules  of  a  piece  of  matter  as  between 
the  most  distant  stars,  and  that  in  this  one 
medium  all  these  various  influences  are 


RADIATION  185 

transmitted.  Lest,  however,  it  be  supposed 
that  the  ether  is  purely  a  philosophical  way 
of  escape  from  the  unknown,  and  that  we 
know  nothing  of  this  elusive  and  all-per- 
vading medium,  let  us  pause  for  a  moment 
to  consider  the  origin  of  the  energy  which 
animates  nearly  everything  that  moves  on 
this  earth.  The  train  that  rushes  on  its 
journey  bearing  its  hundreds  of  tons  of 
weight  1000  miles  in  the  day,  the  liner 
bearing  its  tens  of  thousands  of  tons  lightly 
across  the  seas,  are  animated  with  the  energy 
that  reached  this  earth,  from  a  place 
90,000,000  miles  away,  as  sunbeams  during 
the  forgotten  ages  of  the  past.  Almost  all  the 
energy,  with  which  the  modern  world  throbs, 
arrived  through  this  medium  which  connects 
us  with  the  stars,  and  the  thought  on  which 
we  stumbled,  considering  the  outflowings 
and  incomings  of  energy  around  a  moving 
charge,  or  current  of  electricity,  underlies 
the  flow  of  all  energy  throughout  the  uni- 
verse. The  luminiferous  ether,  as  it  was 
first  called,  because  it  bore  the  light  across 
intra-stellar  space,  has  at  least  one  very 
definite  characteristic,  which  is  quite  suf- 
ficient to  entitle  it  to  be  considered  as  a 
physical  reality.  It  transmits  light  and, 
so  far  as  is  known,  every  other  influence 


186  MATTER  AND  ENERGY 

which  traverses  it,  at  a  definite  speed — 
185,000  miles  in  the  second.  This  velocity 
is  as  characteristic  of  it  as  the  velocity  of 
sound  in  air,  1200  feet  per  second,  is  char- 
acteristic of  the  atmosphere.  Radiations, 
be  they  light  or  heat,  whatever  their  colour 
or  wave-length,  X-rays,  the  ether-waves 
employed  in  wireless  telegraphy,  magnetic 
disturbances,  whether  they  reach  us  from 
the  sun  as  the  accompaniment  of  solar 
storms,  or  whether,  lastly,  they  circulate 
around  the  space  surrounding  a  wire  in  which 
current  of  electricity  is  being  started  or 
stopped — all  travel  through  space  with  the 
speed  of  light.  Sound  is  the  vibration  of 
the  air,  and  all  the  gamut  of  sounds  and 
noises  are  essentially  air  disturbances  of  the 
same  type.  Radiation  is  the  vibration  of 
the  ether,  and  all  the  various  phenomena 
just  enumerated  are  due  to  electro-magnetic 
changes  accompanying  the  alteration  either 
of  the  speed  or  direction  of  motion  of  elec- 
trons. The  ether,  so  far  as  we  know,  vibrates 
only  in  this  one  way,  and  the  vibrations  are 
transmitted  only  with  one  velocity.  The 
explanation  of  the  inertia  of  the  electron 
embraces  also  the  phenomena  of  radiation 
in  all  its  numerous  forms. 
Electrons  are  a  normal  constituent  of 


RADIATION  187 

matter,  and  are  found  revolving  round  the 
atoms  much  as  the  planets  of  a  solar  system 
do  around  the  central  sun.  The  electrical 
tractation  between  the  electron  and  the 
positively  charged  atom  takes  the  place  of 
gravitation.  The  electrons,  like  the  planets, 
possess  a  period  of  revolution  appropriate 
to  their  distance  from  the  atom.  The  nearer 
they  are  the  faster  they  must  revolve,  the 
law  regulating  the  period  of  revolution  and 
diameter  of  the  orbit  being  completely 
analogous  to  Kepler's  law  for  the  planets. 
But  owing  to  the  minuteness  of  the  atom 
and  the  relative  greatness  of  the  electrical 
tractation  compared  with  gravitation,  the 
periods  of  revolution  of  electrons  are  almost 
inconceivably  short.  These  electrons  revolve 
thousands  of  millions  of  millions  of  times 
per  second,  so  that  it  might  be  supposed 
that  it  would  be  quite  impossible  to  measure 
them.  As  a  matter  of  fact,  no  magnitudes 
in  science  are  known  with  greater  exactitude. 
Consider  the  electron  revolving  round  the 
atom.  At  any  point  of  its  revolution  an 
electro-magnetic  field  of  energy  extends 
around  it,  appropriate  to  its  motion.  When 
it  has  traversed  half  a  revolution  it  is  moving 
at  the  same  speed  as  before,  but  in  exactly  the 
opposite  direction.  Its  attendant  magnetic 


188  MATTER  AND  ENERGY 

field  is  therefore  exactly  reversed  in  direc- 
tion. The  reversal  is  not  a  sudden  but  a 
rhythmic  process  occurring  twice  in  the 
revolution.  At  any  point  in  space  the 
magnetic  field  attains  a  maximum,  dimin- 
ishes to  zero,  reverses  its  direction,  and 
attains  a  maximum  again  equal  and  opposite 
to  the  former  maximum  in  half  a  complete 
revolution.  The  ether  transmits  these  rhyth- 
matic  changes  in  the  field  of  energy  sur- 
rounding a  revolving  electron  outwards 
through  space,  as  always,  at  its  own  peculiar 
velocity,  the  velocity  of  light.  And  these 
rhythmic  movements  of  the  ether,  produced 
by  the  smallest  entity  known  reversing  its 
direction  of  motion  regularly  in  its  orbit 
round  the  relatively  massive  single  atoms 
of  matter  thousands  of  billions  of  times  in 
the  second,  what  inconceivably  delicate  in- 
strument can  it  be  that  science  has  invented 
for  their  detection  and  study?  Ah!  no 
instrument  maker  can  make  such  an  instru- 
ment. It  is  furnished  ready  made  not  only 
to  man  but  to  some  of  the  lowliest  organisms 
that  inhabit  the  world.  The  phenomena 
being  described  is  radiation  and  the  rhyth- 
matic  vibrations  of  the  ether,  if  they  occur 
within  certain  limits  of  frequency,  constitute 
light. 


RADIATION  189 

Instead  of  speaking  of  the  periods  of  revolu- 
tion, it  is  more  usual  to  speak  of  the  wave- 
lengths. The  velocity  of  transmission  is 
always  the  same,  185,000  miles  per  second, 
so  that  since  in  one  second  the  number  of 
complete  wave-lengths  is  the  same  as  the 
period  of  revolution,  and  must  cover  a  dis- 
tance of  185,000  miles  when  placed  end  to 
end,  it  follows  that  the  length  of  the  complete 
wave  is  the  velocity  of  light  divided  by  the 
period.  If  the  period  is  rapid  the  wave-length 
is  short,  and  vice  versa.  For  deep  red-light,  at 
one  end  of  the  visible  scale  of  the  spectrum, 
the  wave-length  is  about  7/10,OOOth  of  a  milli- 
metre (1  mm.  =  1/25  inch);  for  deep  violet 
light,  at  the  other  end,  about  4/10,OOOth  mm. 
Waves  shorter  than  this  in  the  ultra-violet, 
down  to  2/10,OOOth  mm.,  affect  the  ordinary 
photographic  plate,  but  not  the  eye.  To 
these  rays  glass  is  opaque,  but  quartz  and 
fluorspar  remain  transparent,  whilst  for  still 
shorter  waves  even  the  air  and  gases  in 
general  are  no  longer  transparent,  but  absorb 
the  rays,  becoming  "ionised"  as  by  the 
X-rays.  So  that  still  shorter  rays  can  only 
be  studied  in  a  vacuum,  and  fluorite  is  the 
only  transparent  optical  material  available. 
These  ultra-violet  radiations  are  capable  of 
producing  brilliant  fluorescence, — f  or  example, 


190  MATTER  AND  ENERGY 

in  barium  platinocyanide.  The  retina  of  the 
eye  fluoresces  faintly  also,  and  this  accounts 
for  the  fact  that  far  beyond  the  limit  of  the 
extreme  violet  of  the  spectrum,  lines  can  be 
seen  with  a  faint  neutral  or  lavender  tint. 
Longer  waves  up  to  20/10,000th  mm.,  in  the 
infra-red,  can  also  be  studied  by  photog- 
raphy with  specially  prepared  emulsions. 
The  ordinary  emulsion  is  of  course  not 
affected  by  red  or  infra-red  light.  Rock 
salt  is  transparent  to  these  long  rays,  but 
glass  is  more  or  less  opaque,  whilst  ebonite 
in  thin  sheets  is  transparent  even  in  the 
visible  red  region.  If  the  sun  is  viewed 
through  an  ordinary  camera  shutter,  made 
of  thin  sheet  ebonite,  it  may  be  distinctly 
seen  as  a  faint  deep  red  object.  There  is 
one  generalisation  that  can  be  made  about 
transparent  solid  substances.  They  are  all 
fine  electrical  insulators.  Mica,  ebonite, 
glass,  quartz,  amber,  sulphur,  etc.  are  among 
the  most  perfect  insulators  known,  and  all 
exist  in  transparent  or  translucent  forms. 
Metals  and  good  conductors  of  electricity  are 
opaque.  Moreover,  in  those  cases  where  it  is 
possible  to  get  a  transparent  film  of  metal, 
as  can  be  done  with  gold  and  silver  leaf  by 
heating,  the  transparent  form  of  the  metal  is 
found  to  have  lost  its  electric  conductivity. 


RADIATION  191 

This,  no  doubt,  is  connected  with  the  fact 
that  in  insulators  the  electrons  are  anchored  to 
the  molecules  and  can  vibrate  with  them  but 
cannot  move  about,  so  that  when  the  electro- 
magnetic wave  of  light  crosses  them  the 
electrons  vibrate  in  unison  with  the  light,  but 
the  energy  is  not  dissipated  in  moving  them 
bodily. 

The  distinction  between  radiant  heat  and 
light  is  non-existent.  In  being  absorbed  by 
opaque  objects,  radiations  of  all  wave- 
lengths, whether  they  belong  to  the  visible  or 
invisible  region  of  the  spectrum,  are  trans- 
formed into  heat.  Very  small  amounts  of 
radiant  energy  in  the  green  and  yellow 
regions  are  visible  to  the  eye,  and  in  the 
violet  and  ultra-violet  can  affect  the  photo- 
graphic plate,  whereas  our  experience  of  the 
longer  waves  is  usually  confined  to  sufficient 
quantities  to  be  detected  by  their  heating 
effects,  as  radiant  heat.  In  addition,  when  a 
solid  substance  is  gradually  heated,  its  radia- 
tion is  confined  to  these  dark  infra-red  or 
heat  rays,  and  not  until  its  temperature  is 
raised  to  "red-heat,"  about  500°  to  600°  C., 
does  it  begin  to  emit  any  visible  light.  In 
passing  to  the  temperature  of  a  white  heat, 
not  only  are  waves  of  shorter  and  shorter 
light  emitted  as  the  temperature  rises,  but 


192  MATTER  AND  ENERGY 

also  the  radiation  of  the  longer  waves  is 
enormously  increased  at  the  same  time,  so 
that  even  white-hot  bodies  give  out  far  more 
energy  as  dark  heat-rays  than  as  visible 
light-rays.  In  astronomy  the  distance  to 
which  the  spectrum  of  a  star  extends  into  the 
violet  region  is  used  as  a  measure  of  the 
temperature  of  the  star.  Even  the  eye 
distinguishes  red  or  comparatively  cool  stars 
like  Betelgeuze  from  blue  or  hot  stars  like 
Vega.  For  every  temperature  of  a  heated 
substance,  there  is  one  particular  wave- 
length of  which  more  radiant  energy  is 
emitted  than  of  any  other.  When  glowing 
substances  of  higher  and  higher  temperature 
are  examined,  it  is  found  that  the  maximum 
emission  of  energy  shifts  regularly  farther 
and  farther  along  the  infra-red  region  towards 
the  visible  region  of  the  spectrum. 

An  extraordinary  case  occurs  in  this  con- 
nection of  what  the  unsophisticated  person, 
who  commented  upon  the  fact  that  large 
towns  always  occur  on  navigable  rivers, 
would  term  Providence.  The  sun  is  probably 
a  red  or  comparatively  cool  star,  but  its 
temperature,  estimated  at  6500°  Centigrade, 
is  incomparably  greater  than  the  highest, 
about  3500°,  attainable  on  earth  even  in 
the  electric  furnace.  For  such  high  tern- 


RADIATION  193 

peratures  the  maximum  amount  of  radiant 
energy  is  no  longer  situated  in  the  infra-red 
or  dark  heat  region,  but  is  for  the  solar 
temperature  in  the  visible  region  between  the 
yellow  and  the  green,  at  the  point,  that  is  to 
say,  of  maximum  sensitiveness  of  our  eyes. 
What  can  this  mean,  but  that  the  human  eye 
has  adapted  itself  through  the  ages  to  the 
peculiarities  of  the  sun's  light,  so  as  to  make 
the  most  of  that  wave-length  of  which  there 
is  most.  For  a  star  cooler  than  the  sun  the 
maximum  of  energy  would  be  toward  the  red, 
for  one  hotter  than  the  sun  toward  the  violet. 
Hence  if  these  suns  have  planets  peopled 
with  inhabitants,  their  eyes,  if  they  adapt 
themselves,  as  ours  seem  to  have  done,  to 
suit  the  prevailing  conditions,  would  be 
most  sensitive  to  red  or  violet  respectively, 
and  the  yellow  green  of  the  spectrum  which 
appears  so  vivid  to  us  would  be  to  them 
relatively  dull.  Let  us  indulge  for  a  moment 
in  those  gloomy  prognostications,  as  to  the 
consequences  to  this  earth  of  the  cooling  of 
the  sun  with  the  lapse  of  ages,  which  used  to 
be  in  vogue,  but  which  radioactivity  has  so 
rudely  shaken.  Picture  the  fate  of  the 
world  when  the  sun  has  become  a  dull  red- 
hot  ball,  or  even  when  it  has  cooled  so  far 
that  it  would  no  longer  emit  light  to  us. 


194  MATTER  AND  ENERGY 

That  does  not  at  all  mean  that  the  world 
would  be  in  inky  darkness  and  that  the  sun 
would  not  emit  light  to  the  people  then 
inhabiting  this  world,  if  any  had  survived 
and  could  keep  themselves  from  freezing. 
To  such,  if  the  eye  continued  to  adapt  itself 
to  the  changing  conditions,  our  blues  and 
violets  would  be  ultra-violet  and  invisible, 
but  our  dark-heat  would  be  light,  and  hot 
bodies  would  be  luminous  to  them  which 
would  be  dark  to  us.  One  can  hardly  emerge 
from  such  thoughts  without  an  intuition 
that,  in  spite  of  all,  the  universal  Life 
Principle,  which  makes  this  world  a  teeming 
hive,  may  not  be  at  the  sport  of  every  physical 
condition,  may  not  be  entirely  confined  to  a 
temperature  between  freezing  and  boiling- 
point,  to  an  oxygen  atmosphere,  to  the  most 
favourably  situated  planet  of  a  sun  at  the 
right  degree  of  incandescence,  as  we  are 
almost  forced  by  our  experience  of  life  to 
conclude.  Possibly  the  Great  Organiser  can 
operate  under  conditions,  where  we  could 
not  for  an  instant  survive,  to  produce  beings 
we  should  not,  without  a  special  education, 
recognise  as  being  alive  like  ourselves. 

The  mathematician's  way  of  expressing  a 
change  of  velocity  is  to  say  that  the  velocity 
is  accelerated,  and  this  strictly  scientific 


RADIATION  195 

use  of  the  term  acceleration  includes  the 
stopping  or  retardation  of  motion,  and  the 
change  of  direction  of  motion,  as  well  as 
the  mere  increase  of  speed  signified  by  the 
current  use  of  the  word  in  ordinary  speech. 
Radiation  is  the  consequence  of  the  accelera- 
tion of  an  electron  in  the  scientific  sense. 
An  electron  revolving  round  an  atom,  like 
a  planet  round  a  sun,  experiences  a  constant 
acceleration  towards  the  centre,  and  the 
radiation  is  rhythmatic  and  regular  so  long 
as  the  orbit  of  the  electron  remains  the 
same,  thousands  of  billions  of  precisely 
similar  waves  following  each  other  out  into 
space  every  second.  We  have,  however, 
already  had  to  consider  a  far  simpler  case 
than  this.  The  electrons  of  the  highly 
exhausted  X-ray  tube  suddenly,  in  full 
flight,  strike  an  obstacle  made  of  the  densest 
possible  material.  Their  course  is  suddenly 
arrested  and  they  are  brought  to  rest.  Let 
us  fix  our  attention  on  a  single  electron  in 
full  flight.  We  know  that  surrounding  it 
there  is  the  appropriate  field  of  energy. 
The  next  instant  the  electron  has  struck 
the  anti-cathode  and  has  been  brought  to 
rest.  The  field  of  energy  around  it  suddenly 
changes.  The  ether,  however,  cannot  in- 
stantaneously transmit  this  change.  If  a 


196          MATTER  AND  ENERGY 

long  straight  line  of  soldiers  in  open  formation 
is  sweeping  regularly  across  a  plain  and  an 
officer  at  one  end  cries  "Halt!"  the  soldier 
next  to  him  halts  instantly  at  the  word  of 
command,  if  he  is  an  "ideal"  soldier,  that 
is  to  say,  and  possesses  no  inertia.  But  the 
man  at  the  other  end  of  the  line,  say  three 
hundred  yards  away,  however  instantane- 
ously he  obeys  the  word  of  command  when 
he  receives  it,  does  not  receive  it  till  about 
one  second  after  it  has  been  given,  which 
is  the  time  taken  for  the  sound  to  travel. 
In  reviews  of  troops  in  open  formation  the 
sound  wave  may,  as  it  were,  be  seen  dis- 
tinctly travelling  along  the  line.  In  exactly 
the  same  way  the  order  radiates  from  the 
suddenly  arrested  electron,  outward  through 
space  with  the  velocity  of  light  in  single 
wave  or  pulse.  But  there  is  no  rhythmal 
or  periodic  succession  of  waves  as  in  light. 
The  bombardment  of  the  anti-cathode  by 
the  electrons  which  produces  the  X-ray  is, 
compared  with  light,  like  the  noise  of  the 
patter  of  hail  on  a  roof  compared  with  a 
musical  note  of  sound.  The  next  illustra- 
tion of  the  radiation  attending  the  accelera- 
tion of  electrons  is  the  Hertz  waves  used  in 
wireless  telegraphy,  but  space  forbids  their 
detailed  consideration. 


RADIOACTIVITY  197 

CHAPTER  IX 

RADIOACTIVITY 

UNTIL  1896,  the  observed  facts  of  science 
were  in  agreement  with  the  view  that  the 
atom  was  the  ultimate  limit  of  material  sub- 
division, and  that  in  no  known  changes, 
chemical  or  physical,  including  in  the  latter 
term  electrical  and  electro-chemical,  did 
the  atoms  belie  their  designation  as  the 
ultimate  foundation-stones  out  of  which  the 
whole  material  universe  was  built  up.  Nega- 
tive electrons  came  to  be  recognised  as 
particles  smaller  than  the  atom,  and  opinions 
were  expressed  that  in  some  unknown  way 
atoms  were  compounded  out  of  these  elec- 
trons. The  philosophical  explanation  of  the 
inertia,  or  mass,  of  electrons  raised  the  ques- 
tion whether  the  mass  or  inertia  of  matter  was 
essentially  different  from  that  of  electricity. 
The  possibility  was  present,  therefore,  that, 
if  by  some  means  the  overpowering  pellation 
of  electrons  could  be  neutralised,  and  a  very 
great  number,  many  thousands  or  hundreds 
of  thousands  as  the  case  may  be,  could  be 
crowded  together  into  the  space  occupied  by 
an  atom,  that  might  be  the  atom  and  matter 


198  MATTER  AND  ENERGY 

as  a  separate  existence  might  be  referred  to 
a  condensed  form  of  electricity.  The  progress 
of  science  has  moved  away  from  this  simple 
conception.  Positive  electrons,  which  were 
postulated  as  the  "cement,"  whereby  the 
pellation  of  the  negative  electrons  might  be 
neutralised,  has  remained  merely  a  term  to 
explain  the  supposed  condensation  of  elec- 
tricity into  matter,  and  has  as  yet  no  physical 
or  experimental  basis  of  existence.  In  addi- 
tion two  sorts  even  of  negative  electrons 
have  had  to  be  postulated.  The  one,  free 
electrons,  which  move  freely  among  the 
atoms  of  matter,  can  be  withdrawn  from 
or  added  to  atoms,  without  the  necessity  of 
supposing  that  the  atom,  as  a  separate 
entity,  has  thereby  been  essentially  altered, 
or  has  ceased  to  exist  as  such.  The  other 
kind  consists  of  the  purely  hypothetical 
"structural  electrons"  out  of  which  the  atoms 
themselves,  by  hypothesis,  are  really  built 
up.  The  electric  charges  which  make  their 
appearance  on  the  rubber  and  the  object 
rubbed  in  frictional  electricity,  it  would  be 
altogether  far-fetched  to  regard  as  derived 
from  the  disappearance  from  existence  of 
the  equivalent  amount  of  matter.  Gradually 
all  the  known  phenomena  due  to  electrons, 
even  the  lines  of  the  spectra  of  elements, 


RADIOACTIVITY  199 

which  at  one  time  it  was  thought  revealed 
its  most  intimate  internal  construction,  have 
been  associated  with  the  first  kind  of  electron, 
which  pursue  a  joint  existence  with  the  atoms, 
much  as  the  attendant  satellites  or  planets 
do  in  reference  to  their  central  suns.  The 
second  class,  in  other  words,  the  atoms 
themselves,  remain,  as  they  were,  untouched 
by  these  advances.  There  are  still  eighty  or 
more  distinct  types  of  elements,  each  with  a 
specific  type  of  atom  or  smallest  particle, 
which  as  yet  can  neither  be  expressed  in 
terms  of  one  another,  nor  of  anything  more 
fundamental.  On  the  other  hand,  a  totally 
distinct  experimental  science,  radioactivity, 
has  grown  up  since  1896,  which  derives 
first  hand  from  Nature,  most  important 
and  astonishing  evidence  of  the  properties  of 
these  atoms,  which  till  then  had  been  entirely 
unsuspected  and  unpredicted  by  the  theories 
of  physical  science.  Events  have  proved 
that  chemistry  is  not  the  most  fundamental 
knowable  science  of  matter,  and  that  changes 
are  proceeding  slowly  and  spontaneously  in 
certain  atoms,  those  of  the  elements  exhibit- 
ing the  new  property  of  radioactivity,  which 
are  totally  distinct  from  the  kinds  of  change 
which  have  hitherto  been  studied. 

The  discovery  of  the  property  of  radio- 


200          MATTER  AND  ENERGY 

activity,  by  Becquerel  in  Paris  in  1896,  was, 
experimentally,  closely  related  to  that  of 
the  X-rays  by  Rontgen  in  1905.  Becquerel 
examined  certain  fluorescent  substances,  that 
is,  substances  which  have  the  power  of 
absorbing  light  and  other  radiations  and  of 
re-emitting  it,  changed  to  a  colour  char- 
acteristic of  the  fluorescent  substance,  rather 
than  of  the  kind  of  radiation  by  which  it 
is  produced.  By  good  fortune  he  included 
certain  of  the  salts  of  uranium,  which  fluor- 
esce  with  a  beautiful  greenish  yellow  hue. 
He  so  discovered  that  these  substances  emit 
also  new  kinds  of  rays,  which,  like  the  X-rays, 
traverse  opaque  substances  like  cardboard 
and  thin  metal  foil  and  affect  the  photo- 
graphic plate.  Continuing,  he  proved  that 
the  new  rays  had  nothing  to  do  with  the 
property  of  fluorescence,  but  were  a  constant 
entirely  new  property  of  the  element  ura- 
nium, exhibited  under  all  circumstances  in  un- 
altering  degree  by  all  its  compounds  and  by 
the  element  itself.  Uranium  is  distinguished 
among  the  elements  as  the  last  member  of 
the  Periodic  System.  It  has  the  heaviest 
atom  of  all  the  elements  and  its  atomic 
weight  is  238.5,  when  that  of  oxygen  is 
taken  at  16.  Mme.  Curie  made  an  examina- 
tion of  all  the  known  elements  or  their  com- 


RADIOACTIVITY  201 

pounds,  to  see  if  this  new  property  was 
possessed  by  any  others  than  uranium. 
She  found  that  thorium,  the  next  heaviest 
element,  with  atomic  weight  232.5,  possesses 
a  similar  property.  None  other  of  the  known 
elements  are  radioactive.  But  the  natural 
ores  of  uranium,  the  minerals  such  as  pitch- 
blende, in  which  this  element  is  found  in  the 
earth,  possess  a  greater  degree  of  radio- 
activity than  can  be  accounted  for  by  the 
uranium  therein  contained.  The  same  has 
since  been  found  true  for  the  thorium  min- 
erals. She  proved  that  part  only  of  the  radio- 
activity is  due  to  uranium,  and  that  other 
new  radioactive  elements,  in  excessively 
minute  quantity,  are  present.  One  of  these, 
happily  given  the  name  "radium,"  after 
many  years  of  patient  work  was  separated 
from  the  mineral,  and  its  compounds  were 
prepared  in  the  pure  state.  Its  atomic 
weight  proved  to  be  226,  the  next  highest 
to  thorium,  and  in  its  whole  chemical  nature 
it  was  just  what  might  have  been  expected 
from  the  Periodic  Classification  of  an  element 
with  this  atomic  weight.  It  resembles  very 
closely  barium  and  the  other  members  of 
this  family,  strontium  and  calcium.  The 
compounds  of  this  group  of  elements  are 
well  known;  for  example,  lime  is  the  oxide 


202  MATTER  AND  ENERGY 

of  calcium,  but  the  elements  themselves  are 
very  reactive  metals  which  are  difficult  to 
isolate  from  their  compounds.  Last  year, 
however,  she  succeeded  in  isolating  the 
element  radium,  and  it  proved  to  be  a  metal 
very  similar  to  barium,  so  far  as  its  mere 
chemical  nature  is  concerned.  The  amount 
of  radium  in  good  pitchblende  is  little  more 
than  one  part  in  ten  million.  Ten  tons  of 
pitchblende  thus  contain  only  1  gram  of 
pure  radium,  and  in  spite  of  the  interest 
awakened,  the  total  amount  of  radium  that 
.  has  ever  been  prepared  probably  does  not 
exceed  10  grams  or  about  ^rd  of  an  ounce. 
Yet,  even  in  pitchblende,  the  radioactivity 
contributed  by  the  radium  greatly  exceeds 
that  due  to  the  uranium.  The  pure  radium 
compounds  are,  weight  for  weight,  many 
millions  of  times  more  radioactive  than 
those  of  uranium  or  thorium,  and  many 
remarkable  properties  are  exhibited  by  them 
which  uranium  and  thorium,  on  account  of 
the  feebleness  of  their  radioactivity,  do  not 
show.  Radium  gives  a  characteristic  spec- 
trum distinct  from  any  other  known  sub- 
stance, and  connected,  by  certain  mathe- 
matical relations  between  the  wave-lengths 
of  its  lines,  with  the  spectra  given  by  barium, 
strontium,  and  calcium.  This  is  of  the 


RADIOACTIVITY  203 

highest  importance,  for  it  establishes  the 
title  of  radium  to  be  considered  a  new  element 
beyond  all  question.  If  radium  is  no  true 
element,  then  the  word  "element"  has  no 
meaning. 

At  the  outset  it  may  make  the  matter 
clearer  if  it  is  stated  that  the  chemistry  of 
the  radio-elements,  uranium,  thorium,  rad- 
ium, etc.,  is  in  no  way  exceptional,  but  that, 
superimposed  upon  their  chemical  properties 
and  totally  unconnected  with  them,  the 
elements  exhibit  an  entirely  new  set  of 
properties,  which  may  be  termed  the  radio- 
active properties.  The  radioactivity  is  a 
property  of  the  atom,  and  neither  the  par- 
ticular compound  in  which  the  atom  is 
combined,  the  physical  state  or  conditions, 
such  as  temperature,  concentration,  etc., 
nor  the  past  history  of  the  substance,  have 
any  real  influence  upon  it. 

In  considering  these  radioactive  properties, 
the  nature  of  the  rays,  emitted  by  the  radio- 
elements,  first  calls  for  remark.  In  this 
department  the  pioneer  was  Rutherford. 
The  general  methods  of  studying  the  new 
radiations  are  similar  to  those  employed  for 
the  X-rays.  First,  the  rays  affect  the  photo- 
graphic plate;  secondly,  they,  when  suf- 
ficiently intense,  excite  visible  fluorescence 


204  MATTER  AND  ENERGY 

in  the  well-known  fluorescent  substances 
already  described;  and  lastly,  they  "ionise" 
the  air.  The  air  is  normally  an  almost 
perfect  insulator.  A  gold  leaf  electroscope, 
when  charged,  retains  its  charge  for  hours 
or  days,  in  spite  of  the  fact  that  it  is  being 
bombarded  incessantly  by  the  countless 
molecules  of  the  air.  But  if  traversed  by 
X-rays  or  by  any  of  the  new  rays,  even  also 
by  light  of  exceptionally  short  wave-length, 
the  air  absorbs  the  rays  and  suffers  a  change. 
The  neutral  molecules  are  dissociated  into 
oppositely  charged  ions,  and  these  ions  carry 
the  electricity  through  the  air,  so  that  it 
becomes  a  partial  conductor.  A  gold-leaf 
electroscope  is  discharged  by  X-rays  and 
the  rays  from  radioactive  substances,  and 
this  property  has  proved  of  the  utmost 
service,  for  upon  it  an  accurate  system  of 
measurement  has  been  based.  It  may  be 
stated  that  any  of  the  new  rays  are  easier 
to  deal  with  quantitatively  than  common 
light  is,  because  their  intensity  is  readily 
and  accurately  measurable  by  electrical  in- 
struments, like  the  gold  leaf  electroscope. 

Three  kinds  of  rays  are  distinguishable, 
termed  Alpha  or  a-rays,  Beta  or  /3-rays,  and 
Gamma  or  7-rays.  The  yS-rays  are  the  ones 
most  obvious  on  first  examination,  for  they 


RADIOACTIVITY  205 

affect  the  photographic  plate  powerfully  and 
are  capable  of  traversing  metal  foils.  Their 
penetrating  power  is  somewhat  less  than 
that  of  the  average  X-rays,  but  it  is  sufficient 
to  be  remarkable.  The  7-rays  are  very 
feeble  by  comparison,  and  very  active  prep- 
arations are  necessary  to  exhibit  them. 
But  their  penetrating  power  is  by  far  the 
greatest  of  any  known  kind  of  ray.  The 
7-rays  of  radium  traverse  half  an  inch  of 
lead  before  being  half-absorbed,  and  other 
substances,  roughly  in  proportion  to  their 
density.  The  fluorescent  effects  of  the  @- 
and  7-rays  are  best  shown  with  willemite 
and  the  platinocyanides.  The  a-rays  are 
among  the  most  feebly  penetrating  of  the 
new  kinds  of  radiation,  and  are  absorbed  by 
a  single  sheet  of  paper  or  by  a  few  inches 
of  air.  Nevertheless  they  are  by  far  the 
most  important  class,  and  possess  over 
95%  of  the  energy  evolved  from  radio- 
active substances.  They  produce  very  power- 
ful ionising  action  and  also  brilliant  fluor- 
escence in  zinc  sulphide,  diamond,  etc.,  but 
their  photographic  action  is  relatively  feeble, 
and  their  effect  on  the  fluorescers,  which 
show  best  the  #-  and  7-rays,  is  small. 

The  0-  and  7-rays  are  believed  to  stand  in 
a  relationship  similar  to  that  of  the  cathode- 


206  MATTER  AND  ENERGY 

rays  and  X-rays  already  discussed.  The 
£-rays  are  free-flying  single  negative  elec- 
trons, but  their  velocity  is,  in  some  cases, 
almost  that  of  light  itself,  the  fastest  velocity 
known.  They  are  deviated  by  a  magnet  just 
like  the  cathode-rays,  but  less  easily  on  ac- 
count of  their  much  greater  kinetic  energy. 

When  these  rays  impinge  upon  atoms  of 
matter,  they  are  all,  more  or  less,  according 
to  their  nature,  absorbed,  and  their  kinetic 
energy,  as  always,  is  transferred  to  the 
molecules  of  matter  and  becomes  heat.  The 
heat  so  generated  by  pure  radium  compounds 
is  extraordinary,  considering  the  minute 
quantities  of  radium  which  are  available. 
Every  hour  radium  generates  sufficient  heat 
to  raise  the  temperature  of  its  own  weight 
of  water  from  the  freezing-point  to  the 
boiling-point.  In  one  day  the  energy  gener- 
ated is  sufficient  to  decompose  its  own  weight 
of  carbon  dioxide  into  carbon  and  oxygen, 
and,  in  thirty-eight  hours,  its  own  weight  of 
water  into  hydrogen  and  oxygen.  These 
are  among  the  most  energetic  chemical 
reactions  known.  Yet,  year  after  year,  since 
the  substance  was  discovered,  radium  has 
been  pouring  forth  this  steady  stream  of 
energy  and  shows  no  sign  of  failing.  In 
ten  years  the  energy  generated  equals  that 


RADIOACTIVITY  207 

developed  in  the  combustion  of  over  a 
thousand  times  its  weight  of  pure  carbon, 
and  more  than  this  of  any  ordinary  fuel. 
Yet  these  supplies  of  energy  continue  un- 
abated and  unaffected  by  any  considerations 
whatever.  There  is  no  way  of  turning  the 
stream  on  and  off  as  it  is  wanted.  This 
property  of  continuously  evolving  energy  is  as 
much  an  essential  part  of  the  nature  of  radium 
as  their  unalterability  in  the  fire  is  a  property 
of  the  noble  metals. 

How  are  these  discoveries  to  be  reconciled 
with  the  law  of  the  conservation  of  energy, 
and  with  the  view  that  energy  is  a  definite 
physical  existence  which  must  come  from 
somewhere  if  continually  generated?  They 
have  been  reconciled  completely,  but  the 
explanation  involves  the  view  that  the  atom 
of  the  chemist,  although  still  the  ultimate 
limit  of  subdivision  of  matter  in  every  arti- 
ficially engendered  process,  is  not  the  natural 
limit.  This  explanation  was  put  forward 
ten  years  ago  by  Rutherford  and  the  writer, 
and  has  since  been  adopted.  In  the  naturally 
occurring  phenomenon  of  radioactivity  there 
is  a  spontaneous  process  continuously  going 
on,  in  which  the  atoms  themselves  are  the 
units  that  change.  The  oft-quoted  words 
of  Clerk  Maxwell,  before  the  British  Associa- 


208          MATTER  AND  ENERGY 

tion  in  1873,  are  no  longer  true.  He  said: 
"Natural  causes,  as  we  know,  are  at  work 
which  tend  to  modify,  if  they  do  not  at  length 
destroy,  all  the  arrangements  and  dimensions 
of  the  earth  and  the  whole  solar  system.  But 
though  in  the  course  of  ages  catastrophes 
have  occurred  and  may  yet  occur  in  the 
heavens,  though  ancient  systems  may  be 
dissolved  and  new  systems  evolved  out  of 
their  ruins,  the  molecules  out  of  which  these 
systems  are  built — the  foundation-stones  of 
the  material  universe — remain  unbroken  and 
unworn."  In  present-day  nomenclature  the 
word  "atoms"  must  be  substituted  for 
"molecules"  in  this  quotation,  for  before 
the  discovery  of  radioactivity  even  the 
most  eminent  physicists  had  not,  like  chem- 
ists, learned  clearly  to  distinguish  between 
atoms  and  molecules.  The  dissolution  of 
ancient  systems  and  the  evolution  of  new 
ones  out  of  their  ruins,  referred  to  so  elo- 
quently by  Clerk  Maxwell,  are  in  all  prob- 
ability controlled  by  the  dissolution  of  their 
atoms.  The  infinitely  slow  march  of  cos- 
mical  evolution  probably  keeps  pace  with 
the  gigantic  periods  of  time  which  these 
atomic  changes  require. 

If  radium,  the  element,  is  the  source  of  the 
energy  it  pours  out  in  a  continuous  stream, 


RADIOACTIVITY  209 

radium,  the  element,  must  change,  and  the 
change  of  an  element  is  transmutation.  The 
position  of  the  parts  constituting  the  atom 
must  alter,  and  the  energy  associated  with 
the  atom  must  suffer  conversion  into  the 
energy  of  motion,  which  ultimately  appears 
and  can  be  measured  as  heat.  Evidence  of 
these  changes  was  soon  forthcoming,  and  now, 
complicated  as  some  of  them  are,  every  detail 
almost  of  the  process,  whereby  the  energy  is 
evolved,  is  known  to  a  degree  of  accuracy 
unsurpassed  in  many  of  the  older  examples  of 
material  change.  Several  reasons  exist  for 
this.  Radioactivity  is  an  inevitable  process, 
which  is  quite  independent  of  the  conditions 
and  circumstances,  and  indeed  is  not  known 
to  be  really  affected  in  the  slightest  degree 
by  any  circumstance  whatever.  Whereas 
chemical  changes,  notoriously,  are  far  less 
simple,  and  are  affected  and  sometimes 
reversed  by  a  great  variety  of  conditions, 
many  of  which  are  still  only  very  imperfectly 
understood.  In  the  second  place,  the  elec- 
trical methods  of  measurement  employed  are 
of  unsurpassed  delicacy  and  certainty,  and 
the  changes  occurring  in  a  quantity  of  radio- 
active matter,  which  in  a  few  minutes  or 
seconds  is  easily  detectable  by  these  methods, 
might  have  to  continue  for  geological  epochs 


210  MATTER  AND  ENERGY 

of  time  before  they  produced  any  effect  that 
could  be  detected  by  the  ordinary  methods  of 
chemistry.  But  the  most  important  reason 
of  all  is  that  the  changes  of  radium  and  the 
other  radio-elements  are,  on  the  one  hand, 
neither  gradual  changes  of  the  atom  in  which 
all  the  atoms  slowly  evolve  their  energy  and 
slowly  change  into  new  forms,  nor,  on  the 
other,  are  they  completely  sudden  processes 
in  which  the  individual  atoms  give  up  their 
store  of  energy,  changing  at  one  step  into  the 
product  or  products.  The  changes  in  radio- 
activity are  of  the  latter  type  exclusively, 
but  they  are  not  single.  If  the  atoms  of 
radium  changed  suddenly  into  their  final 
products  evolving  their  store  of  energy  in  one 
stage,  such  a  process  would  be  difficult  to 
identify.  True,  the  energy  would  sufficiently 
indicate  the  change,  but  it  would  remain 
the  sole  indication.  The  proportion  of  the 
radium  changing  in  a  year  or  in  ten  years 
is  altogether  too  small  to  be  detectable  by 
ordinary  methods  with  the  minute  quantities 
so  far  available,  whilst  in  uranium  and 
thorium,  the  radioactivity  of  which  is  millions 
of  times  feebler  than  that  of  radium,  the  rate 
of  the  change  is  correspondingly  smaller. 
This  is  of  reality  a  necessity,  as  a  little  con- 
sideration will  show.  Radioactivity  is  a 


RADIOACTIVITY  211 

natural  spontaneous  process  occurring  in 
known  materials  at  a  constant  rate.  The 
earth  has  existed,  according  to  geological 
evidence,  for  hundreds  of  millions  of  years  in 
much  the  same  state  as  at  present,  and  if 
radioactivity  is  a  change  occurring  in  certain 
elements,  these  elements  must  long  ago  have 
disappeared  from  the  earth  altogether,  unless 
the  changes  were  slow  even  as  compared  with 
the  progress  of  geological  time.  There  is  only 
one  way  by  which  such  changes  could  come 
within  the  range  of  experimental  science,  and 
that  is  the  way  in  which  the  radio-elements 
actually  have  been  proved  to  be  changing. 

There  is  usually  a  long  succession  of  sepa- 
rate sudden  changes,  part  of  the  energy  being 
evolved  at  each  change.  In  consequence 
there  exist,  intermediate  between  the  initial 
element,  radium,  for  example,  and  its  final 
product,  the  element  lead,  as  is  generally 
supposed  but  not  yet  proved,  a  number  of 
intermediate  forms  of  matter  having  an 
existence  more  or  less  transitory,  but,  in 
spite  of  their  infinitesimal  quantity,  evolving 
so  much  energy  in  their  further  changes  that 
they  can  readily  be  detected  and  accurately 
studied.  Nearly  thirty  of  these  new  transi- 
tional forms  of  radioactive  matter  have  been 
recognised  in  the  changes  of  the  elements 


212          MATTER  AND  ENERGY 

uranium,  thorium,  radium,  and  actinium, 
and  considerations  of  space  alone  would 
prevent  the  detailed  consideration  of  the 
enormous  number  of  important  investigations 
that  have  been  published  upon  them  in  the 
last  ten  years.  It  must  suffice  to  take  one 
example,  the  first  change  of  radium  itself, 
in  some  detail,  as  all  the  others  are  strictly 
analogous  in  their  general  character. 

The  radioactivity  of  a  radium  compound 
appears  to  consist  under  ordinary  circum- 
stances of  all  three  types  of  rays  in  unchang- 
ing proportions.  It  is  sufficient  to  dissolve 
the  compound  in  water  and  to  evaporate  the 
solution  to  dryness  again,  or  even,  more 
simply,  strongly  to  heat  the  compound 
without  dissolving  it,  to  remove  by  far  the 
greater  part  of  this  radioactivity.  A  few 
hours  after  this  treatment,  the  activity  of  the 
radium  is  at  a  minimum  and  no  further 
chemical  or  physical  treatment,  however 
elaborate,  further  alters  it.  At  this  stage 
the  /3-  and  7-rays  have  been  entirely  removed, 
whilst  the  a-rays  have  been  diminished  to 
one-fourth  of  their  initial  amount.  The 
substance  radium  has  not  been  at  all  altered 
by  the  process.  In  the  course  of  time  the 
solid  compound  of  radium  or  its  solution,  if 
kept  in  an  air-tight  vessel,  recovers  the 


RADIOACTIVITY  213 

activity  it  has  lost.  All  the  three  types  of 
rays  are  regenerated  at  characteristic  rates, 
and  in  a  month  it  is  as  radioactive  as  initially. 
These  operations  may  be  repeated  with  the 
same  result  any  number  of  times.  A  closer 
examination  reveals  the  fact  that  during  the 
solution,  or  heating,  a  gaseous  substance, 
called  the  radium  emanation,  escapes.  If 
arrangements  are  made  to  collect  this  gas,  it 
will  be  found  that,  generally  speaking,  the 
whole  of  the  radioactivity  the  radium  has 
lost  is  possessed  by  the  gas.  The  gas  itself 
is  in  almost  absolutely  infinitesimal  quantity. 
Yet  its  radioactivity  is  so  powerful  that  no 
difficulty  whatever  is  experienced  in  detect- 
ing and  working  with  it,  for  it  may  be  mixed, 
if  necessary,  with  air  and  then  dealt  with 
by  ordinary  methods.  In  the  solid  radium 
compound  many  of  the  rays,  particularly  the 
powerful  a-rays,  are  absorbed  by  the  material 
itself,  but  in  the  gas  they  have  full  scope,  and 
the  fluorescent  action  which  the  emanation 
produces  on  bodies  such  as  zinc  sulphide,  is 
remarkably  brilliant. 

The  radium  emanation  itself  shares  with 
the  argon  gases  the  property  of  not  entering 
into  chemical  combination  or  being  absorbed 
by  any  known  reagent.  It  is  also  condensed 
to  the  non-gaseous  form  at  the  temperature 


214  MATTER  AND  ENERGY 

of  liquid  air,  and  in  these  ways  it  is  possible 
to  separate  it  from  all  known  substances  and 
to  study  it  pure.  Then  the  extraordinary 
minuteness  of  its  actual  quantity  and  the 
power  of  its  radioactivity  become  evident. 
From  a  gram  of  pure  radium  the  gaseous 
emanation  obtained  occupies  a  volume, 
measured  under  standard  conditions  of  tem- 
perature and  pressure,  of  only  0.6  of  a  cubic 
millimetre,  the  volume  of  an  ordinary  pin's 
head.  Yet  the  rays  from  far  less  than  a 
thousandth  part  of  this  quantity  will  cause 
zinc  sulphide  to  fluoresce  in  a  way  that  will 
be  plainly  visible  in  an  absolutely  dark  hall 
to  an  audience  of  a  thousand  people.  Indeed, 
if  one-thousandth  of  the  emanation  obtain- 
able from  a  gram  of  radium  were  mixed 
uniformly  with  the  air  of  a  very  large  hall, 
say  with  100,000  cubic  feet,  or  over  3  tons 
by  weight,  of  air,  no  delicate  instrument 
such  as  is  customarily  employed  in  the 
measurement  of  radioactivity  could  be  worked 
in  the  hall,  and  the  amount  in  a  single  cubic 
inch  of  the  air  could  still  be  detected  by  a 
sensitive  gold  leaf  electroscope.  The  unit 
adopted  in  certain  scientific  work  is  the 
amount  of  emanation  produced  by  one  mil- 
lion-millionth of  a  gram  of  radium,  a  quantity 
which  itself  has  a  volume  of  less  than  a 


RADIOACTIVITY  215 

million-millionth  of  a  cubic  millimetre,  and 
weighs  a  million  million  times  less  than  an 
exceptionally  delicate  chemical  balance  will 
turn  to.  Such  a  quantity  contains  less  than 
a  million  single  atoms.  It  is  almost  incredible, 
but  nothing  in  science  is  better  established. 

The  heat  evolved  from  this  emanation  of 
radium  is  in  proportion  to  its  radioactivity. 
The  quantity  of  emanation  derived  from 
1  gram  of  radium  evolves  three-fourths  of 
the  total  given  by  the  radium,  and  when  it  is 
removed  from  the  radium,  the  latter  only 
gives  one-fourth  of  what  it  gave  before. 
Now  it  is  almost  incredible  in  any  case  that  a 
quantity  of  less  than  a  cubic  millimetre  of 
gas  can  evolve  spontaneously  enough  heat  to 
raise  the  temperature  of  three-fourths  of  a 
gram  of  water  from  freezing-point  to  boiling- 
point  in  an  hour.  To  obtain  a  single  cubic 
inch  of  this  gas,  measured  under  standard 
conditions,  would  require  26  kilograms  of 
pure  radium.  This,  therefore,  is  almost  an 
impossibly  large  quantity  practically  to 
obtain,  but  it  is  interesting  to  note  that  the 
energy  such  a  quantity  would  emit  would 
be  equal  to  that  of  a  powerful  electric  arc 
lamp.  The  mystery  of  the  source  of  the 
energy  of  radium  is  increased  a  million-fold 
when  the  nature  of  its  emanation  is  studied. 


tl«          MATTER  AND  ENERGY 

How  long  can  such  an  unparalleled  evolution 
of  energy  last? 

This  is  just  where  the  interesting  point 
comes  in.  The  emanation  of  radium  does 
not  last.  It  is  not  an  apparently  permanent 
source  of  energy  like  the  radium  from  which 
it  originates.  If  the  activity  of  some  radium 
emanation,  sealed  up  in  a  tube,  is  examined 
from  day  to  day,  it  will  be  found  steadily  to 
decay.  In  four  days  its  activity  is  only 
half  the  initial.  In  eight  days  it  is  one 
quarter,  and  so  on.  In  a  month  it  has  all 
practically  disappeared.  But  while  these 
changes  are  taking  place  a  concomitant  set 
are  going  on  in  the  radium  from  which  the 
emanation  was  derived.  It  recovers  the 
activity  it  lost,  when  the  emanation  was 
removed,  just  as  fast  as  the  activity  of  the 
removed  emanation  decays.  If  at  the  end 
of  the  month,  when  the  radium  has  fully 
regained  its  activity,  it  is  redissolved  in  water, 
a  new  quantity  of  emanation  is  obtained  just 
as  great  as  at  first.  Radium  is  producing 
the  emanation.  The  emanation  of  radium 
is  the  first  product  of  the  change  of  the 
radium  atom.  This  emanation  in  its  turn  is 
changing  comparatively  quickly.  The  change 
is  complete  in  a  month.  One-fourth  of  the 
energy  is  derived  from  the  change  of  the 


RADIOACTIVITY  217 

radium,  and  three-fourths  from  the  sub- 
sequent changes  suffered  by  the  emanation. 

Thus,  when  a  quantity  of  radium  is  observed 
to  be  apparently  pouring  forth  in  an  un- 
diminished  stream  its  rays  and  its  energy, 
year  after  year,  what  is  really  taking  place  is 
not  so  simple.  One-fourth  of  the  a-rays  result 
from  the  change  of  some  of  the  radium  atoms 
into  atoms  of  the  emanation.  Three-fourths 
of  the  a-rays  and  the  whole  of  the  /3-  and  7- 
rays  result  in  the  comparatively  rapid  changes 
of  the  emanation  and  its  products,  which  it 
is  unnecessary  particularly  to  specify  here. 
The  steady  outpouring  of  rays  is  due  to  a 
balance  or  equilibrium,  when  as  many  atoms 
of  emanation  are  produced  per  second  from 
the  radium  as  change  per  second  into  other 
substances.  Thus  the  amount  of  emanation 
present  and  the  radioactivity  of  the  radium 
tend  to  become  and  remain  constant  when 
this  equilibrium  is  attained. 

Now  it  is  a  simple  matter  to  calculate 
from  the  equilibrium  amount  of  emanation 
in  any  quantity  of  radium,  and  from  its  rate 
of  change,  both  of  which  data  can  be  directly 
observed,  how  much  emanation  is  being 
produced  from  the  radium  in  a  given  time, 
and  therefore  the  rate  at  which  the  radium 
itself  is  changing  in  producing  this  emanation. 


218  MATTER  AND  ENERGY 

These  calculations  and  numerous  others 
from  entirely  independent  data  lead  to  the 
result,  which  is  probably  not  more  than  a  few 
per  cent,  in  error  at  most,  that  in  one  year 
1 /2500th  part  of  the  radium  changes.  In 
other  words,  the  average  period  of  life,  the 
time,  that  is,  which  a  radium  atom  exists 
on  the  average  before  it  changes,  is  2500 
years.  The  average  period  that  the  atom 
of  emanation  exists  is  only  5.3  days.  Rather 
less  than  one-fifth  of  the  whole  changes  per 
day. 

It  is  now  possible  to  calculate  the  total 
amount  of  energy  that  a  given  quantity  of 
radium  will  evolve  during  its  complete  change, 
which,  of  course,  requires  thousands  of  years. 
We  have  seen  that  in  thirty-eight  hours  the 
energy  is  equal  to  that  required  to  decompose 
its  own  weight  of  water  into  hydrogen  and 
oxygen.  In  the  total  life  of  2500  years  the 
energy  evolved  would  therefore  suffice  to 
decompose  over  half  a  million  times  its 
weight  of  water.  In  this  decomposition 
more  energy  is  required,  weight  for  weight 
of  substance  decomposed,  than  in  any  other 
chemical  reaction.  Or,  the  result  may  be 
expressed  by  saying  that  1  gram  of  radium 
evolves  in  its  complete  change  as  much 
energy  as  a  quarter  of  a  ton  of  coal  does 


RADIOACTIVITY  219 

when  it  combines  with  the  oxygen  of  the 
air  and  burns. 

At  once  arises  a  question:  If  the  period 
of  average  life  of  radium  is  only  2500  years, 
how  is  it  that  there  is  any  radium  still  in 
existence?  Historical  records  go  back  to 
many  times  this  period.  Even  if  the  whole 
world  were  originally  pure  radium  100,000 
years  ago,  the  quantity  now  present  should 
be  less  than  that  actually  contained  in  the 
common  rocks  and  soils  constituting  its 
crust.  The  answer  will  be  found  by  asking 
how  it  is  that  there  is  any  radium  emanation 
in  existence,  as  this  substance  has  a  period 
of  average  life  of  only  5.3  days.  Just  as 
the  quantity  of  radium  emanation  is  main- 
tained in  constant  proportion  to  the  radium 
producing  it,  so  if  there  existed  in  the 
minerals  in  which  radium  is  found  a  much 
more  slowly  changing  element,  in  the  change 
of  which  radium  was  produced,  the  mainte- 
nance of  radium  would  be  explained.  Now 
radium  is  found  in  uranium  minerals.  Ura- 
nium is  radioactive  and  is  therefore  changing. 
But  into  what?  Exact  experiments  have 
shown  that  the  quantity  of  radium  in 
minerals  is  proportional  to  the  quantity 
of  uranium.  There  are  certain  exceptions, 
but  these  can  be  explained  by  the  influences, 


220  MATTER  AND  ENERGY 

such  as  percolating  water,  to  which  rocks 
in  the  earth  are  subjected,  and  which  may 
dissolve  certain  constituents  preferentially. 
Excluding  these  few  cases,  in  all  minerals 
there  is  always  about  3,000,000  times  as 
much  uranium  as  radium.  Experiments 
have  also  been  going  on  for  many  years 
to  see  whether  uranium  preparations,  ini- 
tially quite  free  from  radium,  produce 
radium  in  the  course  of  time.  These  have 
not  yet  produced  a  definite  result.  It  is 
known  that  the  change  of  uranium  into 
radium  is  not  direct,  but  that  an  inter- 
mediate substance,  ionium,  which  does  pro- 
duce radium  steadily  with  the  lapse  of 
time,  intervenes.  The  average  life  of  ionium 
is  probably  at  least  a  hundred  times  longer 
than  that  of  radium.  So  that  direct  attempts 
to  establish  the  production  of  radium  from 
uranium  necessarily  require  a  very  long 
time  to  give  a  definite  result.  There  is, 
however,  very  little  doubt.  The  constancy 
of  proportion  between  uranium  and  radium 
in  minerals  can  only  be  accounted  for  on 
the  view  that  the  former  produces  the  latter. 
Just  as  the  period  of  average  life  of  radium 
can  be  deduced  from  that  of  the  radium 
emanation  and  the  equilibrium  proportion 
between  the  two  substances,  so  also  can  the 


RADIOACTIVITY  221 

period  of  uranium  be  calculated.  There 
are  3,000,000  parts  of  uranium  to  one  part 
of  radium  in  minerals.  Therefore,  it  can 
be  proved,  the  period  of  average  life  of 
uranium  is  3,000,000  times  that  of  radium, 
or  7500  million  years.  But  this  gigantic 
period  agrees  very  well  with  the  extremely 
feeble  radioactivity  of  uranium.  The  latter 
is  many  millions  of  times  less  than  that  of 
radium,  and  therefore  the  substance  must 
be  changing  many  millions  of  times  more 
slowly.  Inordinately  long  as  this  period 
seems  to  be,  compared  even  with  those 
customarily  dealt  with  in  geology,  it  is 
necessary  to  explain  many  aspects  of  cos- 
mical  evolution,  as  will  later  be  dealt  with. 
The  difficulty  with  the  older  physicists 
was  to  allow  geologists  sufficiently  extended 
periods  of  time  for  the  processes  they  studied. 
The  utmost  it  used  to  be  possible  to  allow 
them,  without  trespassing  the  bounds  of 
physical  possibility,  as  it  was  then  under- 
stood, the  geologists  rejected  with  scorn  as 
utterly  insufficient  even  for  a  brief  portion 
of  recent  geological  history.  That  was  before 
these  processes  of  radioactivity  were  known 
in  which  the  energy  evolved  is  a  quarter  of  a 
million  or  more  times  greater  than  in  any 
previously  known  process.  At  least  there 


222  MATTER  AND  ENERGY 

is  no  difficulty  in  accounting  for  the  main- 
tenance of  radium  from  uranium  for  periods 
of  tens  of  thousands  of  millions  of  years, 
without  of  necessity  being  compelled  to 
suppose  that  the  quantity  of  uranium  in 
the  earth  is  being  in  some  still  unknown 
way  maintained.  Geological  time,  even,  does 
not  trace  back  the  history  of  the  earth  to 
periods  so  distant  that  the  quantity  of 
uranium  then  in  existence  must  have  been 
very  appreciably  greater  than  now.  That 
being  so,  it  would  be  profitless  to  speculate 
in  the  present  state  of  knowledge  as  to  the 
origin  of  uranium. 

The  essential  features  of  these  new  pro- 
cesses are  that  the  quantities  of  the  elements 
undergoing  change  are  almost  inconceivably 
minute,  so  that  were  it  not  that  the  new 
changes  of  matter  are  accompanied  by 
proportionally  enormous  changes  of  energy, 
they  would  necessarily  be  quite  unknow- 
able. If  the  change  of  the  matter  is  rapid, 
its  quantity  is  excessively  minute.  If  the 
matter  is,  like  uranium,  not  altogether 
scarce,  the  changes  are  excessively  slow  and 
the  radioactivity  of  the  matter  proportion- 
ately feeble.  It  is  an  old  world,  and  any  but 
the  slowest  primary  changes  must  long  ago 
have  run  their  course.  From  this  point  of 


RADIOACTIVITY  223 

view  the  elements  of  the  Periodic  Classification 
are  those  which  have  survived  because  they 
are  stable.  At  the  extreme  end,  the  elements 
uranium  and  thorium,  though  not  entirely 
permanent  and  stable,  are  yet  changing  so 
slowly  that  some  still  survive.  In  the  light 
of  these  researches  and  the  known  fact  that 
the  elements  of  atomic  weight  between  220 
and  240  are  not  entirely  stable,  but  are 
slowly  changing,  the  abrupt  end  of  the 
Periodic  Table  with  the  element  uranium, 
reads  like  an  interrupted  record  in  which 
the  writer  in  the  last  few  words  had  succeeded 
hi  conveying  a  hint  of  the  approaching  end. 

Slow  as  these  new  processes  are,  and 
infinitesimal  as  are  the  actual  quantities  of 
the  radio-elements  undergoing  change  even 
in  the  most  favourable  cases,  yet  the  ordinary 
methods  of  chemistry  and  spectroscopy  have 
not  proved  entirely  inadequate  in  confirm- 
ing them.  It  may  be  mentioned  that,  in 
the  most  favourable  case,  the  spectroscope 
requires  a  thousand  million  times  greater 
quantity  of  matter  than  can  be  detected 
easily,  for  example,  in  the  case  of  the  radium 
emanation.  The  changes  in  radioactivity 
are  studied  by  means  of  the  energy  evolved. 
A  totally  different  problem  has  to  be  faced 
when  the  chemical  nature  of  the  matter 


224  MATTER  AND  ENERGY 

finally  resulting,  for  example,  in  the  change 
of  radium,  is  the  subject  of  inquiry.  The 
difference  is  analogous  to  that  between 
observing  a  meteor  and  trying  to  find  it 
afterwards,  to  discover  the  nature  of  the 
materials  remaining  when  its  flight  is  spent. 
It  is,  of  course,  a  great  help,  when  the 
chemical  constituents  of  a  substance  are 
under  investigation,  to  have  at  least  some 
idea  of  what  is  likely  to  be  found  if  looked 
for.  In  radioactivity  a  very  simple  process 
of  reasoning  served  to  provide  this  clue. 
Radioactive  changes  are  slow,  but  they  are 
continuous.  In  the  minerals  in  which  the 
radio-elements  occur  these  changes  have 
been  in  operation  for  geological  epochs  of 
time.  Hence  the  ultimate  products  must 
be  present  as  the  invariable  companions  of 
the  radio-elements,  and  the  older  the  geolog- 
ical formation  from  which  the  mineral  is 
derived  the  greater  ought  to  be  the  quantity 
of  these  products  in  the  mineral. 

As  soon  as  the  radioactive  minerals  were 
examined  from  this  point  of  view,  a  very 
striking  fact  transpired.  These  minerals 
contain  the  gas  helium,  though  how  it  got 
there  and  why  it  should  occur  only  in  minerals 
containing  the  elements  uranium  and  tho- 
rium, had  remained  one  of  the  unexplained 


RADIOACTIVITY  325 

mysteries  of  science.  The  name  helium  is 
derived  from  the  Greek  word  for  "the  sun." 
The  most  prominent  line  in  the  spectrum  of 
helium,  a  brilliant  yellow  line  very  close  to  the 
two  well-known  sodium  lines,  had  been  ob- 
served in  the  spectrum  of  the  solar  chromo- 
sphere long  before  the  element  itself  was 
known.  Helium  was  discovered  on  the  earth 
in  certain  minerals  by  Sir  William  Ramsay 
before  the  property  of  radioactivity  was 
known,  and  he  had  noticed  that  the  minerals 
which  contained  it  contained  also  the  ele- 
ments uranium  and  thorium.  But  helium  is 
one  of  the  family  of  monatomic  gases  which 
are  completely  inert  and  do  not  form  com- 
pounds. Neither  are  they  absorbed  chemi- 
cally by  any  substances  whatever.  More- 
over, helium  is  of  all  gases  the  most  difficult 
to  liquefy.  Its  critical  temperature,  or  tem- 
perature below  which  it  cannot  be  liquefied 
under  any  pressure,  however  great,  is  but  a 
very  few  degrees  from  the  absolute  zero. 
What  then  is  the  origin  of  this  uncondensible, 
unabsorbable  gas  in  minerals  containing 
uranium  and  thorium?  The  answer  suggested 
itself  at  once  as  soon  as  the  view  that  radio^ 
activity  was  the  manifestation  of  the  spon- 
taneous change  of  elements.  It  was  predicted 
that  helium  was  one  of  the  unknown  ultimate 


226          MATTER  AND  ENERGY 

products  of  the  changes.  Being  formed  in 
the  solid  mass  of  the  minerals,  which  are 
often  of  a  glassy  nature,  it  is  unable  to 
escape,  and  remains  imprisoned  until  the 
mineral  is  dissolved  or  heated.  Once  liber- 
ated it  cannot  be  put  back.  Then  experi- 
ments with  radium,  by  Sir  William  Ramsay 
and  the  writer,  proved  directly  that  radium 
is  actually  producing  the  gas  helium,  just 
as  we  have  seen  it  is  producing  the  gaseous 
emanation.  Minute  quantities,  sufficient, 
however,  to  be  identified  beyond  any  doubt 
by  the  spectroscope,  were  obtained  from 
radium  preparations  which  had  been  kept 
for  a  few  months  after  manufacture.  On 
solution  in  water  this  helium  was  liberated 
along  with  the  emanation.  Then  helium 
was  proved  to  be  generated  from  the  emana- 
tion. If  the  latter  was  prepared  pure,  by 
condensation  by  means  of  liquid  air  and  other 
treatment,  and  sealed  up  in  a  spectrum  tube, 
the  helium  spectrum  gradually  developed 
in  the  tube  as  the  emanation  changed. 
Later  direct  experiments  have  established 
that  helium  is  the  product  of  most  of  the 
radioactive  elements.  It  has  been  so  ob- 
tained from  actinium,  uranium,  thorium,  and 
polonium. 

But  from  the  very  first,  before  these  direct 


RADIOACTIVITY  227 

experiments,  evidence  had  been  obtained  that 
probably  the  a-rays  consisted  of  swarms  of 
material'  atoms,  projected  with  a  velocity 
hitherto  never  observed.  Rutherford  was 
successful  in  deviating  them  by  a  very 
powerful  magnet,  and  established  that  the 
deviation,  besides  being  almost  incomparably 
smaller  than  that  suffered  by  the  /3-rays,  is  in 
the  opposite  direction.  This  indicated  that 
the  a-rays,  like  the  #-rays,  consist  of  swarms 
of  free  flying  charged  particles,  but  that  their 
charge  is  not  negative,  like  that  of  the  elec- 
tron, but  positive.  True  to  its  character, 
whenever  positive  electricity  is  observed,  it  is 
not,  like  the  negative  variety,  alone,  but  is 
attached  to  material  atoms.  By  methods 
analogous  to  those  discussed  for  the  electron 
or  cathode  particle,  Rutherford  deduced,  from 
the  amount  the  a-ray  was  deflected  by  mag- 
netic and  electric  fields  of  known  strength, 
their  veolocity,  their  mass,  and  their  charge. 
After  many  years'  continuous  effort,  all  three 
data  were  obtained  separately.  The  velocity 
is,  in  the  various  cases,  between  1/1 5th  and 
l/20th  of  that  of  light.  Heretofore  the  fastest 
known  moving  material  thing  was  the  meteor, 
some  of  which  attain  a  speed  of  40  miles 
a  second.  This  is  only  1 /300th  of  that 
of  the  a-particles,  some  of  which  travel 


*28          MATTER  AND  ENERGY 

with  the  speed  of  12,000  miles  a  second. 
The  evidence  at  first  with  regard  to  the  mass 
and  the  charge  enabled  only  a  ratio  to  be 
obtained.  This  indicated  that  if  the  charge 
were  a  single  atomic  charge  of  electricity, 
or,  in  other  words,  if  the  a-particle  were 
analogous  to  the  manovalent  hydrogen  or 
silver  ions  previously  discussed,  the  mass 
of  the  particle  was  twice  that  of  the  hydrogen 
atom.  Whereas,  if  it  were  a  divalent  ion, 
its  mass  would  be  four  times  that  of  the 
hydrogen  atom.  The  latter  is  the  atomic  mass 
of  helium. 

To  settle  this  point,  some  exceedingly 
delicate  experiments  were  performed.  The 
methods  of  measurement  were  so  improved 
that  they  were  sensitive  enough  to  detect 
the  expulsion  of  a  single  a-particle,  or  the 
disintegration  of  a  single  atom  of  radium. 
Under  suitable  conditions  it  was  found  possi- 
ble actually  to  count  the  number  of  a-parti- 
cles  expelled  from  a  known  quantity  of  radium 
in  a  known  time.  This  last  step  enabled  the 
charge  of  the  individual  a-particle  to  be 
measured.  This  proved  that  the  a-particle 
carries  two  atomic  charges.  Its  mass  there- 
fore is  4,  the  same  as  the  atomic  mass  of  the 
helium  atom.  In  every  known  case  where 
a-rays  are  given  by  radioactive  substances, 


RADIOACTIVITY  229 

they  have  been  proved  to  be  atoms  of  helium 
expelled  with  very  great  velocity  and  kinetic 
energy.  One  of  the  most  beautiful  demon- 
strations ever  performed  finally  established 
the  identity  of  a-particles  with  helium  atoms. 
The  a-particle,  although  it  is,  on  account 
of  its  relatively  much  greater  size,  far  less 
penetrating  than  the  y8-particle,  nevertheless 
does  penetrate  a  certain  very  small  thickness 
of  matter.  It  is  possible  to  blow  glass  so 
excessively  thin  that  the  a-particles  can 
pass  through  the  glass,  although  the  glass 
film  retains  to  the  full  its  imperviousness  to 
the  molecules  of  a  gas.  Tubes  were  con- 
structed of  glass  of  this  degree  of  thinness 
of  the  wall,  and  were  fitted  into  an  outer 
vessel.  It  was  shown  that  when  the  tubes 
were  filled  with  ordinary  helium  none  what- 
ever leaked  through  into  the  outer  vessel. 
But  when  filled  with  radium  emanation, 
which  gives  a-particles,  these  can  pass  through 
the  glass,  and  helium  was  then  found  in  the 
outer  vessel  by  means  of  the  spectroscope. 
Thus  beyond  any  possibility  of  doubt  the 
nature  of  the  a-particle  was  established. 

It  is  known  that  three  a-particles,  or 
helium  atoms,  are  expelled  in  the  change  of 
a  uranium  atom  into  radium,  and  that  in  all, 
including  the  subsequent  numerous  changes 


230  MATTER  AND  ENERGY 

suffered  by  the  radium,  eight  a-particles  are 
expelled.  The  atomic  weight  of  uranium 
is  238.5,  and  if  we  subtract  the  weight  of 
three  a-particles  or  helium  atoms,  which  is 
12,  we  get  the  figure  226.5,  which  is  almost 
exactly  the  value  Mme.  Curie  found  by 
experiment.  If  we  subtract  the  weight  of 
eight  helium  atoms,  or  32,  from  238.5,  we  get 
the  figure  206.5.  If  then  in  the  changes 
of  the  uranium  atom  nothing  else  except 
eight  helium  atoms  are  expelled  (the  mass  of 
the  /S-particles  expelled  is  too  small  to  be  of 
importance),  the  final  product  should  be  an 
atom  of  weight  206.5.  The  nearest  element 
to  this  is  lead,  the  atomic  weight  of  which  is 
207. 

Now  the  same  kind  of  evidence  which  led 
to  the  prediction  that  helium  was  one  of  the 
ultimate  products  has  indicated  that  lead  is 
produced  from  uranium.  Lead  in  important 
quantity  is  a  constant  companion  of  almost 
all  uranium  minerals.  The  older  the  geo- 
logical formation  from  which  the  mineral 
is  derived,  the  higher  the  percentage  of  lead 
appears  to  be.  The  direct  proof  or  disproof 
of  this  view  is  not  yet  accomplished,  but 
experiments  are  now  in  progress,  and  the 
result  may  be  announced  at  any  time.  It 
is  generally  conceded  that  there  is  very  little 


RADIOACTIVITY  231 

doubt  that  lead  is  the  final  stable  form 
assumed  when  the  changes  of  uranium  are 
complete. 

These  investigations,  although  only  in 
their  infancy,  have  thus  thrown  a  flood  of 
light  on  the  nature  of  the  atom.  In  the  few 
cases  in  which  it  is  now  possible  to  watch 
the  process,  the  outstanding  feature  is  the 
altogether  unparalleled  amount  of  potential 
energy  associated  with  the  atomic  structure, 
which  is  released  and  rendered  apparent 
when  the  structure  undergoes  change.  The 
element  helium  seems  to  play  a  predominant 
part  in  the  internal  structure  of  the  radio- 
elements.  Uranium  appears  to  be  made  up 
of  eight  atoms  of  helium  with  one  of  lead, 
and  so  on.  But  atoms  are  not  simply  a 
special  sort  of  chemical  compound  in  the 
ordinary  sense.  There  is  more  difference 
between  the  change  of  an  element,  as  in 
radioactivity,  and  an  ordinary  chemical 
change,  as  in  the  union  of  hydrogen  and 
oxygen  to  form  water,  than  there  is  between 
the  latter  and  a  so-called  physical  change, 
like  the  condensation  of  steam.  It  is  best 
therefore  not  to  be  in  too  great  a  hurry 
to  abolish  the  old  distinction  between  atoms 
and  compounds  of  atoms,  or  to  believe  the 
ancient  theory  that  matter,  though  appar- 


282  MATTER  AND  ENERGY 

ently  diverse,  is  philosophically  simple, 
and  that  all  the  atoms  are  merely  various 
compounds  of  some  primordial  stuff  or 
"protyle."  Such  a  problem  has  now  alto- 
gether too  serious  consequences  for  the  whole 
future  destiny  of  the  race  to  be  lightly 
assumed,  on  account  of  the  philosophical 
edification  it  arouses.  The  advance  of  science 
along  that  road,  which  as  a  matter  of  fact 
never  appeared  so  impassable  as  it  does 
to-day,  would  not  leave  a  single  stone 
standing  of  all  the  elaborate  superstructure 
of  civilisation  as  it  is  at  present  understood. 


CHAPTER  X 

COSMICAL   ENERGY 

EVER  since  the  doctrine  of  energy  became 
established  the  source  of  cosmical  energy  has 
attracted  attention.  Whence  comes  the 
steady  supply  of  solar  radiation  upon  which 
existence  on  this  planet  absolutely  depends? 
How  long  has  it  been  going  on  and  how  long 
will  it  continue?  Vast  as  the  sun  is,  some- 
thing more  than  its  mere  store  of  heat  energy 
is  necessary  to  enable  it  to  continue  emitting 


COSMICAL  ENERGY  288 

its  light  and  heat  at  the  present  rate  for  more 
than  a  very  limited  time.  Even  the  idea 
that  the  sun  is  a  huge  fire  and  derives  its 
heat  from  the  combustion,  or  chemical  com- 
bination of  its  component  materials,  is  alto- 
gether insufficient  to  supply  the  waste  of  heat 
even  over  the  period  covered  by  the  records 
of  history.  The  idea  which  has  found  most 
favour  hitherto  is  that  the  maintenance  of 
the  heat  of  the  sun  is  explained  by  shrinkage 
of  its  materials  into  smaller  volume.  If,  as 
explained  on  p.  40  of  Astronomy  in  this  series, 
the  gravitation  has  not  already  packed  the 
materials  of  the  sun  together  as  closely  as 
they  will  go,  and  every  thousand  years  the 
diameter  shrinks  about  40  miles,  the  kinetic 
energy  resulting  from  the  gravitation  and 
concentration  of  the  materials  would  equal 
that  estimated  to  be  lost  by  radiation.  The 
question  at  once  arises,  "Why  should  the 
sun  shrink  unless  it  is  falling  in  temperature?" 
The  explanation  would  account  for  a  slower 
fall  of  temperature  than  would  occur  if 
shrinkage  did  not  take  place,  but  the  idea 
that  shrinkage  can  maintain  the  temperature 
uniform,  or  nearly  uniform,  seems  inadequate. 
The  heat  so  gained  is,  however,  altogether 
insufficient  on  present  evidence,  and  as  there 
is  no  other  ground  for  believing  that  shrinkage 


234  MATTER  AND  ENERGY 

is  in  fact  taking  place,  it  is  unnecessary  to 
pursue  the  question. 

\Yhat  has  to  be  accounted  for  is  not  the 
maintenance  of  the  sun's  heat  at  uniform 
temperature  for  a  few  million  or  even  one 
hundred  million  years,  but  for  hundreds, 
possibly  thousands  of  millions.  The  geolo- 
gists are  agreed,  and  their  point  is  generally 
admitted,  that  the  surface  of  the  earth  must 
have  remained  in  much  the  same  physical 
conditions  as  at  present  for  these  immense 
periods.  Before  the  discovery  of  radio- 
activity, no  source  of  energy  sufficiently 
abundant  and  lasting  was  known  which  would 
suffice  for  a  period,  at  the  very  most,  of  more 
than  a  hundred  million  years. 

Another  more  definite  line  of  evidence  is 
obtained  from  the  temperature  of  the  earth. 
The  solid  crust  of  the  earth  conducts  heat 
excessively  slowly.  If,  as  was  before  sup- 
posed, the  earth  was  originally  hot  and 
molten  and  has  cooled  on  the  surface  by 
radiation,  it  is  possible,  by  finding  the  tem- 
perature gradient  as  we  descend,  that  is  the 
number  of  feet  on  the  average  which  have  to 
be  descended  for  the  temperature  to  rise  one 
degree,  to  calculate  how  great  a  period  of 
past  time  could  have  elapsed  before  the 
surface  must  have  been  too  hot  to  sustain 


COSMICAL  ENERGY  235 

life.  Arguments  along  these  lines  put  the 
limits  of  the  possible  age  of  the  earth  during 
which  it  has  been  in  a  state  capable  of  sup- 
porting life  on  the  surface,  as  even  less  than  a 
hundred  million  years. 

These  arguments  and  calculations  have  all 
been  completely  altered  in  consequence  of 
the  discovery  of  the  energy  evolved  in  radio- 
activity, when  atoms  undergo  spontaneous 
change.  A  thousand  millionth  of  a  milli- 
gram of  radium  is  about  the  smallest  quantity 
that  can  be  practically  detected.  It  has 
been  found  that  all  the  common  rocks  and 
soils  of  which  the  earth's  crust  is  built  up 
contain  measurable  amounts  of  radium. 
Strutt  has  calculated  from  his  measurements, 
that  if  a  crust  of  the  earth  only  some  50 
miles  thick  contained  the  same  amount  of 
radium  as  the  representative  samples  of  the 
rocks  he  examined,  the  heat  generated  by 
this  radium  would  suffice  to  account  for  all 
the  heat  lost  by  the  earth  by  radiation. 
There  is,  however,  no  reason  to  limit  the 
radium  to  the  surface  crust.  In  addition,  no 
allowance  was  made  in  the  calculation  for 
the  heat  generated  by  the  small  amounts  of 
uranium  and  thorium,  which  more  recent 
investigations  have  shown  are  as  important 
as  the  radium  in  contributing  heat.  Argu- 


236  MATTER  AND  ENERGY 

ment  based  upon  this  evidence  is,  necessarily, 
somewhat  hypothetical,  for,  under  the  enor- 
mous pressures  that  exist  in  the  interior, 
even  radioactive  changes  may  not  run  their 
normal  course.  But  the  day  has  gone  by 
when  the  earth  is  regarded  simply  as  a  cooling 
world.  It  has  in  its  known  material  con- 
stituents a  steady  source  of  fresh  heat,  which 
will  last,  not  for  one  million,  but  for  thousands, 
or  tens  of  thousands  of  millions  of  years.  It 
is  regarded  as  more  probable  to-day,  that 
instead  of  the  earth  becoming  colder  by 
radiation,  as  has  been  supposed,  it  is  steadily 
growing  hotter  and  hotter  in  its  interior. 
The  heat  so  generated  throughout  the  mass, 
on  account  of  the  low  conductivity  of  the 
rocks  and  materials  forming  the  crust,  only 
very  slowly  reaches  the  surface.  At  the 
surface,  the  heat  generated  escapes  by  radia- 
tion and  maintains  the  temperature  uniform. 
But  the  interior  is  almost  completely  ther- 
mally isolated  from  the  surface,  and  the  tem- 
perature within,  provided  that  the  composi- 
tion of  the  materials  is  similar  to  that  on  the 
surface,  must  steadily  be  increasing.  Joly 
has  made  some  interesting  calculations  of 
the  inevitable  results  that  must  attend  such 
a  process.  Assuming  a  quantity  of  radium, 
and  its  corresponding  amount  of  uranium, 


COSMICAL  ENERGY  237 

distributed  uniformly  throughout  the  mass  of 
the  earth,  of  two  parts  of  radium  per  million 
million,  which  is  less  than  the  average  found 
for  surface  rocks,  this  would  produce  an 
increase  in  the  temperature  of  the  interior 
by  1800°  C.  in  a  hundred  million  years.  So 
long  as  the  earth's  crust  remained  solid,  this 
heat  would  only  escape  by  conduction  with 
extreme  slowness.  But  at  some  time  or 
other,  a  world  so  constituted  must  explode, 
when  the  increasing  temperature  and  pres- 
sure within  overpowers  the  strength  of  the 
crust.  According  to  the  same  authority,  there 
is  no  assurance  that  such  a  consummation 
does  not  await  the  future,  nor  evidence  that 
such  has  not  more  than  once  been  an  event 
of  the  past. 

Such  considerations  give  an  idea  of  the 
importance  of  radioactivity  in  cosmical  pro- 
cesses. Over  periods  of  time,  appropriate 
to  the  periods  at  which  these  new  changes 
proceed,  even  minute  proportions  of  uranium 
and  thorium  distributed  throughout  a  world, 
must  inevitably  affect  its  whole  internal 
physical  condition,  apart  altogether  from  the 
influence  of  external  energy  and  of  the  rest 
of  the  system  of  which  it  forms  part.  Its 
history  is  a  function  of  its  diameter,  the 
amount  of  the  radioactive  elements  contained 


£88          MATTER  AND  ENERGY 

in  its  materials  and  the  conductivity  of  the 
latter  for  heat,  at  least  for  periods  of  thousands 
of  millions  of  years.  The  amount  of  thermal 
energy  it  possessed  when  it  originated  would, 
at  least  in  all  but  exceptional  cases,  long 
before  this  have  ceased  to  exert  any  influence 
at  all.  The  primary  sources  of  natural 
energy,  by  virtue  of  which  the  universe  keeps 
going  over  immense  periods  of  time,  are  to 
be  sought  not  in  the  great  masses  of  glowing 
matter  dotted  about  the  heavens,  nor  in  their 
motions  under  the  action  of  gravity,  nor  in 
any  of  the  grosser  relations  between  energy 
and  matter  in  bulk,  but  in  the  individual 
atoms  out  of  which  it  is  made  up.  No  other 
source  is  at  once  sufficiently  abundant  and 
sufficiently  lasting,  probably,  even  for  a 
single  geological  age,  the  period,  that  is, 
since  the  ocean  condensed  and  rain  and  rivers 
began  their  work  of  denudation  and  upbuild- 
ing. Only  a  beginning  has  so  far  been  made 
into  the  study  of  these  new  unsuspected  forms 
of  energy,  but  enough  is  known  to  make  it 
clear  that,  whether  it  be  so  or  not,  radio- 
activity alone,  including  in  that  term  pro- 
cesses involving  atomic  transformations,  is 
competent  to  be  regarded  as  the  mainspring 
of  the  universe. 
Changes  of  this  magnitude,  which  have 


COSMICAL  ENERGY  239 

swept  aside  all  the  prevailing  notions  as  to 
the  origin,  past  age,  and  future  destiny  of 
this  and  other  worlds,  have  not  left  un- 
touched the  questions  nearer  home  concerning 
human  history  and  destiny.  It  is  not  neces- 
sary to  discuss  the  question  here  as  to  how 
far  the  radio-elements  are  alone  in  parting 
with  their  stores  of  internal  energy,  or 
whether,  so  far,  in  radioactivity,  merely  one 
type  has  been  recognised  of  changes  which, 
in  greater  or  less  degree,  may  be  proceeding 
in  all  matter.  From  the  general  similarity 
of  nature  of  the  chemical  elements,  it  can 
be  argued  that  if  one  could  be  artificially 
transmuted  the  way  would  be  opened  for 
the  transmutation  of  others.  The  common 
elements  are  merely  elements  which  are  not 
changing,  but  there  is  the  strongest  reason 
to  believe  that  many  of  them,  if  they  could 
be  changed  into  simpler  forms,  would  give 
out  supplies  of  energy  no  less  remarkable 
than  that  furnished  by  the  radio-elements. 
There  is,  however,  no  evidence  at  present 
that  any  other  of  the  common  elements 
except  uranium  and  thorium  are  capable  of 
spontaneous  change,  and  therefore  nothing 
is  known  of  the  energy  these  other  elements 
may  contain.  It  suffices  merely  to  take 
stock  of  the  new  supplies  of  energy,  in  sight, 


240  MATTER  AND  ENERGY 

so  to  speak,  without  troubling  whether  the 
advance  of  knowledge  will  disclose  more. 
The  conversion  of  thermal  energy  into 
mechanical  energy,  first  practically  effected 
by  the  invention  and  perfection  of  the  steam 
engine,  has  brought  about  in  a  single  century 
more  permanent  change  in  the  manner  of 
living,  and  even  in  the  habits  of  thought 
of  the  inhabitants  of  the  world,  than  any 
combination  of  political,  social,  or  personal 
influences  could  have  effected.  It  is  the 
mastery  of  man  over  Nature,  as  represented 
by  matter  and  energy,  rather  than  that  of 
one  man  over  another,  or  of  one  race  over 
another,  to  which  histories  give  such  exag- 
gerated predominance,  which  underlies  prog- 
ress. What,  therefore,  will  be  the  effect  of 
the  discovery  that,  so  far,  we  have  been 
subsisting  on  the  mere  by-products  of  natural 
energy,  and  have  remained  ignorant  even  of 
the  existence  of  the  primary  supplies  in  the 
atoms  of  matter?  That  it  must  exert  a 
profound  influence  upon  every  department 
of  human  thought  need  scarcely  be  stated. 
The  forgotten  savage  who  kindled  the  first 
artificial  fire  little  knew  the  consequences 
that  were  to  follow.  We  can  form  a  faint 
conception  of  some  at  least  of  the  conse- 
quences which  would  follow  the  introduction 


COSMICAL  ENERGY  241 

of  the  new  sources  of  energy  into  the  practical 
affairs  of  the  world.  But  although  science 
has  discovered  these  new  sources,  it  by  no 
means  can  be  taken  for  granted  that  their 
practical  utilisation  must  follow  as  a  matter 
of  course. 

A  moment's  consideration  will  serve  to 
show  that  although  the  present  problem  of 
how  to  release  for  use  at  will  the  energy  in 
uranium,  thorium,  and  radium  for  practical 
purposes  appears  in  a  new  light,  it  is  in 
reality  one  of  the  most  ancient  problems  to 
which,  from  the  earliest  times,  the  energies 
of  the  race  have  been  unceasingly  and  unsuc- 
cessfully directed.  The  natural  processes  in 
which  the  atomic  energy  is  evolved  are 
necessarily  either  excessively  slow  or  are 
shown  by  compensatingly  minute  quantities 
of  materials.  Along  with  the  discovery  that 
a  pound  of  uranium  contains  and  evolves 
in  its  changes  the  same  amount  of  energy 
as  a  hundred  tons  or  more  of  coal  evolves 
in  its  combustion,  is  the  knowledge  that 
little  more  than  1/10,000,000,000  part  of 
this  is  given  out  every  year.  These  natural 
processes  must  be  controlled  and  made  to 
proceed  much  more  rapidly  than  they  do 
spontaneously  before  any  of  the  new  sources 
of  energy  become  of  the  least  use  in  ordinary 


242          MATTER  AND  ENERGY 

engineering.  The  transformation  of  the  ura- 
nium into  helium  and,  presumably,  lead  must 
be  carried  out  in  an  artificial  manner  before 
the  energy  of  the  process  becomes  available. 
But  this  involves  nothing  less  than  the  trans- 
mutation of  one  element  into  others.  The 
new  problem  is  but  transmutation,  although 
the  alchemists,  and  others  who  have  at- 
tempted to  solve  it,  little  guessed  what  success 
on  their  part  would  have  involved.  We  are 
no  more  competent  to  make  use  of  these 
supplies  of  atomic  energy  than  a  savage, 
ignorant  of  how  to  kindle  a  fire,  could  make 
use  of  a  steam  engine. 

Naturally  all  the  resources  of  modern 
science  have  been  employed  in  the  attempt 
to  influence  radioactive  processes,  to  make 
them  proceed  in  any  way  differently  than 
they  do  naturally,  and  also  to  imitate  them 
in  non-radioactive  materials.  These  attempts 
have  been  signal  failures,  and  indeed  from 
the  energy  point  of  view  they  appear  rather 
like  trying  to  influence  the  course  of  a  bullet 
by  blowing  at  it.  True  to  its  character  as 
a  natural  process  of  transmutation,  radio- 
activity is  altogether  uninfluenced  by  ex- 
ternal conditions.  It  proceeds  at  its  natural 
rate  with  a  detachment  from  and  inde- 
pendence of  its  environment  which  qualifies 


COSMICAL  ENERGY  243 

it  to  be  used  as  an  absolute  standard  of 
time.  Nothing  that  is  known  will  affect  the 
transmutation  of  one  element  into  others, 
and,  appropriately  enough,  nothing  known 
is  competent  to  affect  the  natural  process 
in  those  elements  which  are  undergoing 
spontaneous  transmutation.  It  is  a  mistake 
to  suppose  that  it  is  only  a  matter  of  time 
before  science  succeeds  in  this  quest.  It 
merely  has  to  be  stated  that  the  process  of 
radioactivity  involves  the  expulsion  of  atoms 
of  helium,  with  a  velocity  300  times  greater 
than  ever  previously  known  for  any  material 
mass  or  particle,  to  make  clear  how  little 
hope  there  is  for  a  long  time  either  of  con- 
trolling or  imitating  it.  One  of  the  most 
likely  processes  to  affect  the  rate  of  trans- 
formation of  a  radioactive  substance  would 
be  the  bombardment  to  which  it  is  itself 
subjected  by  the  helium  atoms  expelled 
by  those  of  its  atoms  actually  breaking 
up.  This  means  that  the  rate  of  the  process 
should  be  greater  for  a  concentrated  radium 
preparation  than  for  the  same  element  in  a 
diluted  state,  mixed  with  a  large  quantity 
of  non-radioactive  materials.  But  this  has 
been  found  not  to  be  the  case.  It  cannot 
be  denied  that  the  only  process  known  at 
all  likely  to  be  competent  to  affect  the 


244          MATTER  AND  ENERGY 

stability  of  an  ordinary  atom  is  the  change 
of  a  neighbouring  radioactive  atom.  The 
evidence  so  far,  however,  justifies  the  con- 
clusion that  artificial  transmutation,  or  what 
comes  to  the  same  thing,  the  release  of  the 
energy  associated  with  the  structure  of  the 
atoms  for  practical  purposes,  has  not  yet 
been  brought  appreciably  nearer  by  the 
discovery  of  radioactivity.  The  weapons  of 
the  stone  age  would  be  of  little  use  in  the 
working  of  steel. 

After  all,  what  has  an  atom  to  fear  from 
the  utmost  that  can  be  done  to  it  in  the 
laboratory?  Has  it  not  been  subjected  in 
the  laboratory  of  Nature  to  temperatures 
immeasurably  higher  and  to  pressures  of 
which  science  has  no  conception?  Its  simple 
existence  is  eloquent  of  its  fitness  to  survive. 
Not  without  reason  have  the  atoms  been 
termed  the  foundation  stones  of  the  universe. 
The  title  is  derived  not  from  the  laboratory 
experience  of  chemists  only,  for,  by  the  aid 
of  the  spectroscope,  the  materials  of  the 
most  distant  star  can  be  analysed  into  their 
constituent  elements.  Sun  and  stars  tell 
the  same  story.  The  atoms  out  of  which 
they  are  composed  are  the  same,  with  possibly 
one  or  two  exceptions,  as  those  found  on  the 
earth.  It  seems  almost  presumptuous  to 


COSMICAL  ENERGY  245 

hope  that  the  atoms  which  continue  to  exist 
unchanged  under  conditions  so  transcending 
any  that  can  be  reproduced  in  the  laboratory 
will  ever  by  any  conceivable  advance  of 
science  be  displaced  from  the  proud  position 
they  occupy  in  the  economy  of  Nature. 

Through  metaphysics  first,  then  through 
alchemy  and  chemistry,  through  physical 
and  astronomical  spectroscopy,  lastly  through 
radioactivity,  science  has  slowly  groped  its 
way  to  the  atom.  Through  the  various 
ideas  of  phlogiston,  imponderable  fluids, 
attractions,  repulsions,  affinities,  and  forces, 
science  has  ended  with  the  simple  universal 
conception  of  energy.  The  discovery  of  the 
relation  of  the  atom  to  energy  within  the 
last  decade  recalls  the  strange  mediaeval 
myth  that  the  Philosopher's  Stone,  which 
had  the  power  of  transmuting  metals,  when 
discovered  would  prove  also  to  be  the  Elixir 
of  Life.  Transmutation,  the  pulling  to  pieces 
and  putting  together  of  atoms,  would  render 
available  the  primary  sources  of  energy 
which  maintain  the  time-defying  processes 
of  cosmical  evolution. 

Civilisation,  as  it  is  at  present,  even  on  the 
purely  physical  side,  is  not  a  continuous  self- 
supporting  movement.  The  conditions  under 
which  it  originates  determine  its  period  and 


246          MATTER  AND  ENERGY 

fix  the  date  of  its  decline.  It  becomes 
possible  only  after  an  agelong  accumulation 
of  energy,  by  the  supplementing  of  income 
out  of  capital.  Its  appetite  increases  by 
what  it  feeds  on.  It  reaps  what  it  has  not 
sown,  and  exhausts,  so  far,  without  replenish- 
ing. Its  raw  material  is  energy,  and  its 
product  is  knowledge.  The  only  knowledge 
which  will  justify  its  existence  and  postpone 
the  day  of  reckoning,  is  the  knowledge  that 
will  replenish,  rather  than  further  diminish, 
its  limited  resources.  When  coal  is  ex- 
hausted and  the  other  physical  resources  of 
civilisation  have  all  been  squandered,  when 
expanding  civilisation  is  met  by  a  dwindling 
supply  of  energy,  either  science  or  the  atom 
will  have  been  tested  to  destruction  and  one 
or  the  other  will  be  the  arbiter  of  the  future. 
The  triumphs  of  science  over  Nature  till 
now  resemble  somewhat  schoolboy  successes. 
This  period  is  passing  away.  Its  function  in 
the  future  will  be  not  the  spending  to  good 
purpose  of  what  has  been  provided,  but  the 
provision  of  what  is  being  spent.  It  is 
perfectly  obvious  that,  with  the  whole  planet 
in  measurable  distance  of  being  occupied,  and 
nations  being  concerned  rather  to  preserve 
what  they  have  got  than  to  acquire  more,  a 
turning-point  is  being  reached  in  the  upward 


COSMICAL  ENERGY  247 

progress  which  has  hitherto  kept  pace  with 
the  advancement  of  knowledge.  Thoughts 
of  economy  and  conservation  will  inevitably 
replace  those  of  development  and  progress, 
and  the  hopes  of  the  race  will  centre  in  the 
future  of  science.  So  far  it  has  been  a  fair- 
weather  friend.  It  has  been  generally  mis- 
understood as  creating  the  wealth  that  has 
followed  the  application  of  knowledge.  Mod- 
ern science,  however,  and  its  synonym, 
modern  civilisation,  create  nothing,  except 
knowledge.  After  a  hand-to-mouth  period 
of  existence,  it  has  come  in  for  and  has 
learned  how  to  spend  an  inheritance  it  can 
never  hope  to  restore.  The  utmost  it  can 
aspire  to  is  to  become  the  Chancellor  of 
Nature's  Exchequer,  and  to  control  for  its 
own  ends  the  immense  reserves  of  energy 
which  are  at  present  in  keeping  for  great 
cosmical  schemes. 

It  looks,  therefore,  as  if  our  successors 
would  witness  an  interesting  race,  between 
the  progress  of  science  on  the  one  hand  and 
the  depletion  of  natural  resources  upon  the 
other.  The  natural  rate  of  flow  of  energy 
from  its  primary  atomic  reservoirs  to  the 
sea  of  waste  heat  energy  of  uniform  tempera- 
ture, allows  life  to  proceed  at  a  certain  pace, 
sternly  regulated  by  the  inexorable  laws  of 


248  MATTER  AND  ENERGY 

supply  and  demand,  which  the  biologists 
have  recognised  in  their  field  as  the  struggle 
for  existence.  The  flow  of  energy  is,  how- 
ever, not  a  simple,  straightforward  affair, 
but  proceeds  in  stages  through  intermediate 
reservoirs.  The  main  part  that  concerns  life 
on  this  planet  is  received  as  radiant  energy. 
Part  suffers  useless  conversion  into  its  final 
form  directly;  a  smaller  part  produces, 
through  the  evaporation  of  the  ocean  and 
rainfall,  the  "  white  fuel "  or  water  power  which 
is  more  and  more  being  turned  to  practical 
use;  yet  another  part  in  bygone  days  was 
stored  up  in  the  remains  of  the  forests  of  the 
carboniferous  era,  and,  in  the  form  of  coal, 
furnishes  the  main  supply  in  use  at  the  mo- 
ment. Natural  gas  and  oil  may  represent  a 
residue  of  the  initial  heat  energy  of  the  earth, 
or  even  a  portion  of  that  continually  being 
evolved  by  the  radio-elements.  At  very 
high  temperature,  only  to  be  artificially 
realised  in  the  electric  furnace,  carbon  enters 
into  a  series  of  compounds  with  the  metals 
known  as  the  carbides,  which  are  decom- 
posed by  water,  giving  hydrocarbons.  Acety- 
lene is  merely  one  instance.  Moissan  con- 
siders that  the  natural  deposits  of  petroleum 
and  supplies  of  natural  gas  have  their  origin 
probably  in  the  decomposition,  by  the  action 


COSMICAL  ENERGY  249 

of  percolating  water,  of  carbides  formed  deep 
down  in  the  earth. 

In  so  far  as  it  has  been  found  possible  to 
accelerate  the  pace  of  life,  beyond  that  fixed 
by  the  laws  of  supply  and  demand  of  energy, 
it  has  been  by  utilising  these  accumulated 
supplies  of  energy.  As  already  remarked, 
the  utilisation  of  water  power  is,  in  the  energy 
balance-sheet,  pure  gain.  But  the  small  pro- 
portion of  the  increased  demands  of  civilisa- 
tion so  furnished  is  negligible  as  compared 
with  the  enormous  part  from  the  consumption 
of  coal  and  other  natural  fuel.  It  might  be 
supposed  that  an  almost  unlimited  expansion 
would  be  possible,  as  the  demand  arose,  in 
the  utilisation  of  the  direct  heat  of  the  sun 
or  of  the  energy  of  the  tides.  But  it  is 
doubtful  whether  either  of  these  will  ever 
suffice  to  drive  directly  a  practicable  engine. 
In  their  indirect  application,  in  the  improve- 
ment of  agricultural  processes  by  irrigation, 
in  forestry  and  so  on,  no  doubt  the  future 
will  derive  more  benefit  from  them  than  the 
present.  Sooner  or  later,  but  certainly  not 
indefinitely  later,  nothing  known  will  remain 
to  supplement  the  natural  rate  of  supply 
of  energy,  save  the  primary  stores  of  atomic 
energy  on  the  one  hand  and  the  waste  heat 
energy  of  uniform  temperature  on  the  other — 


250  MATTER  AND  ENERGY 

a  state  of  things  that  might  aptly  be  repre- 
sented by  the  proverb  of  the  devil  and  the 
deep  sea,  so  far  as  any  existing  knowledge 
goes.  It  is  probable  that  the  first  of  these 
alternatives  is  the  less  hopeless,  and  that  the 
problem  of  artificial  transmutation  will  in 
the  future  come  to  be  regarded,  no  longer 
in  the  light  it  was  a  few  years  ago,  as  an 
impossible  chimera  surviving  from  the  dis- 
creditable epoch  in  which  the  science  of 
chemistry  originated,  but  as  the  final  phase 
of  the  agelong  conflict  of  interests  between 
Nature  and  Man.  Success  would  remove  for 
ever  the  physical  limit  to  the  continuous 
advance  of  progress,  and  would  endow  it 
with  a  permanent  significance  which  at 
present  it  does  not  possess.  Failure,  on  the 
other  hand,  would  mean  a  gradual  future 
relapse  of  the  race  into  a  more  primitive 
condition,  and  the  loss  of  much,  if  not  most, 
of  what  distinguishes  life  to-day  from  that  of 
our  unscientific  ancestors. 

It  has  been  stated  that  a  problem  defined 
is,  in  science,  a  problem  more  than  half 
solved.  The  process  of  mental  preparation 
necessary,  before  it  is  clear  that  a  definite 
problem  exists,  often  requires  longer  than 
the  solution  of  the  problem,  once  it  has  been 
recognised.  Possibly  the  difficulties  in  the 


COSMICAL  ENERGY  251 

way  of  transmutation  may  prove  less  for- 
midable than  now  appears.  Time  alone  will 
answer  that  question.  But  it  is  character- 
istic of  the  age  that  a  problem  at  first  sight 
of  purely  philosophical  character,  whether 
matter  is  fundamentally  one  or  of  many 
different  kinds,  should  have  become,  suddenly 
at  the  beginning  of  this  twentieth  century, 
the  problem  of  the  relation  between  Man  and 
external  Nature  in  its  final  and  most  funda- 
mental form.  No  one  to-day  is  ignorant  of 
the  part  played  by  energy,  not  only  in  science, 
but  in  industry,  politics,  and  the  whole  scheme 
of  human  welfare.  From  the  cradle  to  the 
grave  every  one  is  dependent  on  Nature  for 
an  absolutely  continuous  supply  of  energy 
in  one  or  other  of  its  numerous  forms.  When 
the  supplies  are  ample  there  is  prosperity, 
expansion,  and  development.  When  they  are 
not,  there  is  want.  Often,  it  is  true,  energy 
appears  to  play  a  very  subsidiary  and  in- 
direct part  in  the  development,  just  as,  no 
doubt,  the  supply  of  wind  might  be  looked 
upon  as  playing  a  very  secondary  role  in  the 
music  of  an  organ.  The  fact  remains  that,  if 
the  supply  of  energy  failed,  modern  civili- 
sation would  come  to  an  end  as  abruptly  as 
does  the  music  of  an  organ  deprived  of  wind. 
Before  science  had  advanced  to  the  knowl- 


252          MATTER  AND  ENERGY 

edge  of  the  utilisation  of  the  stores  of  energy 
in  fuel,  the  favourite  method  employed  by 
earlier  civilisations  to  augment  their  normal 
supplies  of  available  energy  was  by  means 
of  slaves.  To  their  skill  in  the  utilisation  of 
this  form  of  energy  the  Pyramids  of  Egypt 
bear  witness.  To  a  negro  the  electric  car 
appeared  in  the  light  of  the  emancipation  of 
the  mule.  A  single  machine  nowadays  cus- 
tomarily does  the  work  of  10,000  horses, 
good  typical  British  cart  horses,  and  accom- 
plishes more  work  than  a  whole  army  of 
slaves  could  do.  We  are  fortunate  to  be 
living  in  the  days  of  cheap  coal.  It  has  but 
to  be  kindled  when  the  sunshine  of  forgotten 
times  does,  at  will,  the  work  of  the  world, 
and  the  helot  and  the  negro  walk  free.  If 
we  pause  but  for  a  moment  to  reflect  what 
energy  means  for  the  present,  we  may  gain 
some  faint  notion  as  to  what  the  question  of 
transmutation  may  mean  in  the  future  to  a 
fuelless  world,  once  more  dependent  upon  a 
hand-to-mouth  method  of  subsistence.  It 
may  still  be  centuries  before  this  occurs, 
but  neither  the  application  of  the  discoveries 
of  science  nor  even  their  achievement  is  to  be 
compared  with  the  struggle  in  winning  them. 
It  is  a  satisfaction  peculiar  to  the  present 
age  to  have  learned  that  no  physical  poverty 


COSMICAL  ENERGY  253 

of  Nature  bars  the  road  stretching  away  into 
the  future.  The  world  is  great  enough  and 
rich  enough  to  supply  human  aspirations  and 
ambitions  beyond  all  present  dreams.  But 
the  human  intellect  must  keep  pace  in  its 
development  with  the  expanding  vision  of 
natural  abundance. 


BIBLIOGRAPHY 


Lectures  on  some  Recent  Advances  in  Physical  Science, 
by  P.  G.  Tait  (Macmillan  &  Co.),  though  first  published  in 
1876,  gives  a  very  valuable  account  of  the  development  of  the 
Doctrine  of  Energy  during  the  middle  of  last  century. 

The  Elements,  by  Sir  W.  A.  Tilden  (Harper  &  Bros.,  Library 
of  Living  Thought),  1910,  deals  with  the  Periodic  Law  as  it 
appears  to  the  trained  chemist. 

Brownian  Movement  and  Molecular  Reality,  by  Jean  Perrin, 
translated  by  F.  Soddy  (Taylor  &  Francis,  London),  1910, 
gives  a  vivid  though,  necessarily,  not  entirely  non-mathemati- 
cal account  of  the  way  in  which  the  Brownian  Movement  has 
bridged  the  gap  between  Molecular  and  Thermodynamical 
Science. 

Electrons,  by  Sir  Oliver  Lodge  (Macmillan  &  Co.),  1906, 
and  The  Electron  Theory,  by  E.  E.  Fournier  d'Albe  (Longmans, 
Green  &  Co.),  1906,  may  be  recommended  as  introductions  to 
the  newer  views  in  the  subject  of  Electricity  and  Magnetism. 

The  Corpuscular  Theory  of  Matter,  by  Sir  J.  J.  Thomson 
(C.  Scribner's  Sons),  1907,  gives  an  authoritative  account  of 
the  author's  experiments  and  attempts  to  found  an  Electrical 
Theory  of  Matter. 

Light,  Visible  and  Invisible,  by  Silvanus  P.  Thompson 
(Macmillan  &  Co.),  1897,  contains  a  popular  account  of  the 
nature  of  light  and  X-rays. 

The  Interpretation  of  Radium,  by  Frederick  Soddy  (G.  P. 
Putnam's  Sons),  1909,  deals  popularly  with  the  phenomena 
of  radioactivity,  and  their  explanation  by  the  Theory  of 
Atomic  Disintegration. 

Inorganic  Evolution  as  studied  by  Spectrum  Analysis,  by 
Sir  Norman  Lockyer  (Macmillan  &  Co.),  1900,  and  Worlds  in 
the  Making,  by  Svante  Arrhenius,  translated  by  H.  Borns 
(Harper  &  Bros.),  1908,  discuss  some  of  the  problem*  of  cos- 
mica!  evolution,  the  first  from  the  spectroscopic,  and  the 
second  from  a  general  point  of  view. 

Radioactivity  and  Geology,  by  John  Joly  (D.  Van  Nostrand 
Co.),  1909,  is  a  fascinating  volume,  showing  the  inter-connec- 
tion between  the  two  sciences  indicated  by  the  title. 
254 


INDEX 


Age  of  the  earth,  233 
Atomic  volume,  69 
Atomic  weight,  47,  53,  230 
Avogadro's  Law,  56,  81 

Brownian  movement,  78,  91,  103 

Civilisation,  stability  of,  11,  35, 
245 

Conservation  as  a  Test  of  Real- 
ity, 19,  41 

Conservation  of  Energy,  15,  19, 
27,  207 


Diamond,  45,  132 
Dimensions  of  space,  173,  1! 
Dissociation   of   molecules, 
142 


127, 


Elasticity,  23,  141 
Electric  furnace,  132 
Electrons,  151  et  seq.,  197 
Elements,  28,  38,  51,  58  et  seq. 
Emanation  of  radium,  213 
Energy,  Electro-magnetic,  178 
Energy  of  coal,  15,  18,  31,  35,  37, 

248 

Energy  of  food,  14,  104,  135 
Energy,  Potential  and  Kinetic,  20, 

22,  33,  72,  111 
Equipartition    of   energy,    82    et 

seq.,  126 
Ether,  184  et  aeq. 

Fixation  of  nitrogen,  133  et  seq. 
Foot-pound,  25 
Force,  19,  106 
Fundamental  existences,  42 


Heat,  24,  29,  71  et  aeq.,  191,  206, 

215 
Helium  produced  from  radium, 

224 
Horse-power,  32.  102 

Joule's  Equivalent,  30 

Life  process,  45,  59,  101,  194 
Light,  186  et  aeq. 

Mechanism  of  conversion  of  heat 
into  work,  117 

Nascent  state,  49 

Periodic  Law,  61  et  teq. 
Perpetual  motion,  74  et  »eq. 
Phlogiston,  Theory  of,  27,  130 
Positive  electricity,  149,  152, 168, 


Radium,  201  et  seq. 

Rays  of  radioactive  substances, 

203,  212,  227 
Refrigeration,  97,  118 

Slavery,  252 
Surface  tension,  90 
Synthesis,  44,  45 

Temperature,  84,  121 
Tractation  and  pellation,  110 
Transmutation,  40,  47,  142,  209, 
242 

Unit,  Board  of  Trade,  32,  146 
White  fuel,  131,  136,  248 


Gravitation,  25.  106,  112 


X-rays,  161,  186,  195 


255 


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20.  History  of  Our  Time  (1885-1911). 

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By  SIR  T.  W.  HoLDERNESs.  "The  best  small  treatise  dealing  with  the 
range  of  subjects  fairly  indicated  by  the  title." — The  Dial'. 

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51.  Master  Mariners. 

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A  history  of  the  black  man  in  Africa,  America  or  wherever  else  his 
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partnership or  profit-sharing,  or  both,  and  gives  details  of  the 
arrangements  now  in  force  in  many  of  the  great  industries. 

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the  Present  Day. 

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14.  Evolution. 

By  PROF.  J.  ARTHUR  THOMSON  and  PROF.  PATRICK  GEDDES.  Explains 
to  the  layman  what  the  title  means  to  the  scientific  world. 

23.  Astronomy. 

By  A.  R.  HINKS,  Chief  Assistant  at  the  Cambridge  Observatory. 
"Decidedly  original  in  substance,  and  the  most  readable  and  informa- 
tive little  book  on  modern  astronomy  we  have  seen  for  a  long  time." 

— Nature. 

24.  Psychical  Research. 

By  PROF.  W.  F.  BARRETT,  formerly  President  of  the  Socciety  for 
Psychical  Research,  A  strictly  scientific  examination. 


9.  The  Evolution  of  Plants. 

By  DR.  D.  H.  SCOTT,  President  of  the  Linnean  Society  of  London. 
The  story  of  the  development  of  flowering  plants,  from  the  earliest 
zoological  times,  unlocked  from  technical  language. 

43.  Matter  and  Energy. 

By  F.  SODDY,  Lecturer  in  Physical  Chemistry  and  Radioactivity, 
University  of  Glasgow.  "Brilliant.  Can  hardly  be  surpassed.  Sure 
to  attract  attention." — New  York  Sun. 

41.  Psychology,  The  Study  of  Behaviour. 

By  WILLIAM  McDouGALL,  of  Oxford.  A  well  digested  summary  of 
the  essentials  of  the  science  put  in  excellent  literary  form  by  a  lead- 
ing  authority. 

42.  The  Principles  of  Physiology. 

By  PROF.  J.  G.  MCKENDRICK.  A  compact  statement  by  the  Emeritus 
Professor  at  Glasgow,  for  uninstructed  readers. 

37.  Anthropology. 

By  R.  R.  MARETT,  Reader  in  Social  Anthropology,  Oxford.  Seeks  to 
plot  out  and  sum  up  the  general  series  of  changes,  bodily  and  mental, 
undergone  by  man  in  the  course  of  history.  "Excellent.  So  enthusi- 
astic, so  clear  and  witty,  and  so  well  adapted  to  the  general  reader.** 
— American  Library  Association  Booklist. 

17.  Crime  and  Insanity. 

By  DR.  C.  A.   MERCIER,  author  of  Text-Book  of  Insanity,  etc- 

12.  The  Animal  World. 

By  PROF.  F.  VV.  GAMBLE. 

15.  Introduction  to  Mathematics. 

By  A.  N.  WHITEHEAD,  author  of  Universal  Algebra. 

PHILOSOPHY  AND  RELIGION 
69.  A  History  of  Freedom  of  Thought. 

By  JOHN  B.  BURY,  M.  A.,  LL.  D.,  Regius  Professor  of  Modern  His- 
tory in  Cambridge  University.  Summarizes  the  history  of  the  Ion/ 
struggle  between  authority  and  reason  and  of  the  emergence  of  the 
principle  that  coercion  of  opinion  is  a  mistake. 

55.  Missions :  The'r  Rise  and  Development. 

By  MRS.  MANDELL  CREIGHTON,  author  of  History  of  England.  The 
author  seeks  to  prove  that  missions  have  done  more  to  civilize  the 
world  than  any  other  human  agency. 

52.  Ethics. 

By  G.  E.  MOORE,  Lecturer  in  Moral  Science,  Cambridge.  Discusses 
what  is  right  and  what  is  wrong,  and  the  whys  and  wherefores. 

65.  The  Literature  of  the  Old  Testament. 

By  GEORGE  F.  MOORE,  Professor  of  the  History  of  Religion,  Harvard" 
University.  "A  popular  work  of  the  highest  order.  Will  be  profit- 
able to  anybody  who  cares  enough  about  Bible  study  to  read  a  serious 
book  on  the  subject." — American  Journal  of  Theology 

50.  The  Making  of  the  New  Testament. 

By  B.  W.  BACON,  Professor  of  New  Testament  Criticism.  Yale.  An 
authoritative  summary  of  the  results  of  modern  critical  research 
with  regard  to  the  origins  of  the  New  Testament. 


96.  A  History  of  Philosophy. 

By  CLEMENT  C.  J.  WEBB,  Oxford. 

35.  The  Problems  of  Philosophy. 

By  BERTRAND  RUSSELL,  Lecturer  and    Late   Fellow,  Trinity  College, 

Cambridge. 

44.  Buddhism. 

By  MRS.  RHYS  DAVIDS,  Lecturer  on  Indian  Philosophy,   Manchester. 

46.  English  Sects:  A  History  of  Nonconformity. 

By  W.  B.  SELBIE,  Principal  of  Manchester  College,  Oxford. 

60.  Comparative  Religion. 

By  PROF.  J.  ESTLIN  CARPENTER. 

88.  Religious  Development  Between  Old  and  New 
Testaments. 

By  R.  H.  CHARLES,  Canon  of  Westminster.  Shows  how  religious  and 
ethical  thought  grew  between  180  B.  C.  and  100  A.  D. 

LITERATURE  AND  ART 
73.  Euripides  and  His  Age. 

By  GILBERT  MURRAY,  Regius  Professor  of  Greek,  Oxford 

81.  Chaucer  and  His  Times. 

By  GRACE  E.  HADOW,  Lecturer  Lady  Margaret  Hall,  Oxford;  Late 
Reader,  Bryn  Mawr. 

70.  Ancient  Art  and  Ritual. 

By  JAKE  E.  HARRISON,  LL.  D..  D.  Litt.  "One  of  the  100  most  impor- 
tant books  of  1913." — New  York  Times  Reriew. 

61.  The  Victorian  Age  in  Literature. 

By  G.  K.  CHESTERTON, 

97.  Milton. 

By  JOHN  BAILEY. 

59.  Dr.  Johnson  and  His  Circle. 

By  JOHN  BAILEY*  Johnson's  life,  character,  works,  and  friendships 
are  surveyed;  and  there  is  a  notable  vindication  of  the  "Genius  of 
Boswell." 

58.  The  Newspaper. 

By  G.  BINNEY  DIBBLE.  The  first  full  account,  from  the  inside,  of 
newspaper  organization  as  it  exists  to-day. 

62.  Painters  and  Painting. 

By  SIR  FREDERIC  WEDMORE.     With  16  half-tone  illustration. 

64.  The  Literature  of  Germany. 

By  J.  G,  ROBERTSON. 

48.  Great  Writers  of  America. 

By  W.  P.  TRENT  and  JOHN  ERSKINE,  of  Columbia  University. 

87.  The  Renaissance. 

By  EDITH  SICHEL,  author  of  Catherine  de  Medici,  Men  and  Women 
of  the  French  Renaissance. 

101.  Dante. 

By  JEFFERSON  B.  FLETCHER,  Columbia  University,  An  interpretation 
Vt  Dante  and  his  teachings  from  his  writings. 


93.  An  Outline  of  Russian  Literature. 

By  MAURICE  BARING,  author  of  The  Russian  People,  etc.  Tolstoi, 
Tourgenieff,  Dostoieffsky,  Pushkin  (the  father  of  Russian  Litera- 
ture), Saltykov  (the  satirist),  Leskov,  and  many  other  authors. 

40.  The  English  Language. 

By  L.  P.  SMITH.     A  concise  history  of  its  origin  and  development. 

45.  Medieval  English  Literature. 

By  W.  P.  KER,  Professor  of  English  Literature,  University  College, 
London.  "One  of  the  soundest  scholars.  His  style  is  effective,  sim- 
ple, yet  never  dry." — The  Athenaeum. 

89.  Elizabethan  Literature. 

By  J.  M.  ROBERTSON,  M.  P.,  author  of  Montaigne  and  Shakespeare, 
Modern  Humanists. 

27.  Modern  English  Literature. 

By  G.  H.  MAIR.  From  Wyatt  and  Surrey  to  Synge  and  Yeats,  "One 
01  the  best  of  this  great  series." — Chicago  Evening  Pott. 

2.  Shakespeare. 

By  JOHN  MASEFIELD.  "One  of  the  very  few  indispensable  adjuncts 
to  a  Shakespearean  Library." — Boston  Transcript. 

31.  Landmarks  in  French  Literature. 

By  G.  L.  STRACHEY,  Scholar  of  Trinity  College,  Cambridge.  "It  is 
difficult  to  imagine  how  a  better  account  of  French  Literature  could 
be  given  in  250  pages." — London  Times. 

38.  Architecture. 

By  PROF.  W.  R.  LETHABY.  An  introduction  to  the  history  and  theory 
of  the  art  of  building. 

66.  Writing  English  Prose. 

By  WILLIAM  T.  BREWSTER,  Professor  of  English,  Columbia  Univer- 
sity. "Should  be  put  into  the  hands  of  every  man  who  is  beginning 
to  write  and  of  every  teacher  of  English  that  has  brains  enough  to 
understand  sense." — New  York  Sun. 

83.  William  Morris :  His  Work  and  Influence. 

By  A.  CLUTTON  BROCK,  author  of  Shelley:  The  Man  and  the  Poet. 
William  Morris  believed  that  the  artist  should  toil  for  love  of  his  work 
rather  than  the  gain  of  his  employer,  and  so  he  turned  from  making 
works  of  art  to  remaking  society. 

75.  Shelley,  Godwin  and  Their  Circle. 

By  H.  N.  BRAILSFORD.  The  influence  of  the  French  Revolution  oil 
England. 

OTHER    VOLUMES   IN    PREPARATION 

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